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PUBLICATIONS

Jim Michael Cushing
Professor Emeritus
Department of Mathematics
Interdisciplinary Program in Applied Mathematics
University of Arizona
Tucson, AZ 85721 USA

BOOKS

Cover-Discrete-Math-Models-in-Pop-BiologyMatrix Models for Population, Disease, and Evolutionary Dynamics1. J. M. Cushing, Matrix Models for Population, Disease, and Evolutionary Dynamics, Student Mathematical Library, Volume 106, American Mathematical Society, 2024, ISBN: 978-1-4704-7334-1

2. Saber N. Elaydi and J. M. Cushing, Discrete Mathematical Models in Population Biology: Ecological, Epidemic, and Evolutionary Dynamics, Springer Undergraduate Texts in Mathematics and Technology, Springer Nature Switzerland AG, 2024, 978-3-031-64794-9



ModelingBehaviorAndPopulationDynamics


3. J. M. Cushing, Shandelle M. Henson, and James L. Hayward, Modeling Behavior and Population Dynamics: Seabirds, Seals, and Marine Iguanas, Interdisciplinary Applied Mathematics, Volume 57, Springer Nature, Switzerland, 2023, 978-3-031-34282-0




Chaos in Ecology Cover
4. J. M. Cushing, R. F. Costantino, Brian Dennis, Robert A. Desharnais, and Shandelle M. Henson, Chaos in Ecology: Experimental Nonlinear Dynamics, Theoretical Ecology Series, Volume 1, Academic Press (Elsevier Science), New York, 2003, ISBN: 0-12-1988767

'In terms of what they reveal about the mechanisms of population growth, about nonlinear stage-structured population models, and about chaos in ecology, these experiments are on the level of the classic works of Gause, Nicholson, Park, and Huffaker. In terms of the integration of experiment  and theory, they surpass even those studies. Anyone interested in the dynamics of populations will benefit from reading this book.' - Hal Caswell, Ecology (2003)

'This is the definitive source on chaos in ecology. Well-written and authoritative.' - Simon Levin, Princeton University 2002 

'The authors have made very circumspect model verifications...The greatest merit of the book is that it confirms experimentally the existence of numerous nonlinear phenomena in populations and presents a new characteristic of populations, that is, the lattice effect. The book is written in an excellent style with high mathematical precision. This work is warmly recommended to all theoretical and field ecologists, and all scientists interested in nonlinear dynamics.'' - Community Ecology (2005)

'... rich in statistical concepts and methods. Anyone interested in the dynamics of populations will benefit from reading this book.' - Ecology (2003)

'... an elegant blend of mathematics, statistics, and biology...' - Chance (Fall 2003)

'Chaos in Ecology ought to be read by both field and theoretical ecologists.' - Complex Systems Lab, Barcelona, Spain (2002)

5. J. M. Cushing, An Introduction to Structured Population Dynamics, Conference Series in Applied Mathematics Vol. 71, SIAM, Philadelphia, 1998, ISBN 0-89871-417-6 ERRATA

6. J. M. Cushing, Integrodifferential Equations and Delay Models in Population Dynamics, Lecture Notes in Biomathematics 20, Springer, Berlin Heidelberg New York, originally published in 1977 and reprinted in 2013, ISBN 978-3-642-93073-7

7. J. M. Cushing, Differential Equations: An Applied Approach, Pearson - Prentice Hall, Upper Saddle River, New Jersey 2004, ISBN: 0-13-044930-X

BOOKS IN PREPARTION

  1. Shandelle M. Henson, Robert A. Desharnais, J. M. Cushing, Brian Dennis, R. F. Costantino, Complex Population Dynamics: Theory and Data, Chapman & Hall/CRC, to appear 2025

BOOKS EDITED

  1. Sorin Olaru, Jim. Cushing, Saber Elaydi, and René Lozi, Difference Equations, Discrete Dynamical Systems and Applications, IDCEA 2022, Gif-sur-Yvette, France, June 18-22, Springer Proceedings in Mathematics & Statistics, Volume 444, Springer Cham, 2024
  2. J. M. Cushing, M. Saleem, H. M. Srivastava, M. A. Kahn, and M. Merajuddin, Applied Analysis in Biological and Physical Sciences, Springer Proceedings in Mathematics & Statistics, Volume 186, Springer, India, 2016
  3. Lluis Alseda Soler, Jim M. Cushing, Saber Elaydi, and Alberto Adrego Pinto, Difference Equations, Discrete Dynamical Systems and Applications, Volume 180, Springer Proceedings in Mathematics & Statistics, Springer, Berlin & Heidelberg, 2016
  4. Ziyad AlSharawi, J. M. Cushing, and Saber Elaydi, Theory and Applications of Difference Equations and Discrete Dynamical Systems, Springer Proceedings in Mathematics & Statistics, Vol. 102, Springer, Heidelberg, 2014
  5. S. Elaydi, J. M. Cushing, R. Lasser, V. Papageorgiou, A. Ruffing, W. Van Assche, Difference Equations, Special Functions and Orthogonal Polynomials, World Scientific Publishing Co. Pte. Ltd., Singapore, 2007

JOURNAL ARTICLES

  1. J. M. Cushing, A Darwinian version of the Leslie logistic model for age-structured populations, to appear Mathematical Biosciences and Engineering, 2025
  2. J. M. Cushing, Junpyo Park, Alex Farrell and Nakul Chitnis, Treatment outcome in an SI model with evolutionary resistance: a Darwinian model for the evolution of resistance, Journal of Biological Dynamics, 17:1, (2023), DOI: 10.1080/17513758.2023.2255061
  3. J. M. Cushing and Kathryn Stefanko, A Darwinian dynamic model for the evolution of post-reproduction survival, Journal of Biological Systems 29(2) (2021), 433-450, https://doi.org/10.1142/S0218339021400088
  4. J. M. Cushing, A bifurcation theorem for Darwinian matrix models with an application to the evolution of reproductive life history strategies, Journal of Biological Dynamics 15:sup1 (2021), S190-S213, https://doi.org/10.1080/17513758.2020.1858196
  5. J. M. Cushing, A Darwinian Ricker equation, Progress on Difference Equations and Discrete Dynamical Systems (S. Baigent, M. Bohner, S. Elaydi, editors), Springer Proc. Math. Stat., vol. 341, Springer, Cham, 2020, pp. 231-243, DOI 10.1007/978-3-030-60107-2_10. MR4219152
  6. J. M. Cushing and A. P. Farrell, A bifurcation theorem for nonlinear matrix models of population dynamics, Journal of Difference Equations and Applications 26(1) (2020), 25-44, http://dx.doi.org/10.1080/10236198.2019.1699916
  7. J. M. Cushing, Discrete time Darwinian dynamics and semelparity versus iteroparity, Mathematical Biosciences and Engineering, 16(4) (2019), 1815-1835, DOI 10.3934/mbe.2019088
  8. J. M. Cushing, Stability and the geometry of bifurcation graphs for a class of nonlinear Leslie models, Difference Equations and Discrete Dynamical Systems with Applications, Proceedings in Mathematics & Statistics (M. Bohner, S. Siegmund, R. Hilscher and P. Stehlik, eds.), Springer Nature Switzerland, 2019, pp. 201-211
  9. J. M. Cushing, Difference Equations as Models of Evolutionary Population Dynamics, Journal of Biological Dynamics 13 (2019), 103-127, DOI 10.1080/17513758.2019.1574034
  10. J. M. Cushing and S. M. Henson, Periodic matrix models for seasonal dynamics of structured populations with application to a seabird population, Journal of Mathematical Biology 77 (2018), 1689-1720, DOI: 10.1007/s00285-018-1211-4
  11. S. L. Robertson, S. M. Henson, T. Robertson and J. M. Cushing, A matter of maturity: to delay or not to delay? Continuous-time compartmental models of structured populations in the literature 2000-2016, Natural Resource Modeling 31, No. 1 (2018), 1-26, DOI: 10.1111/nrm.12160
  12. J. M. Cushing, F. Martins, A. A. Pinto, A. Veprauskas, A bifurcation theorem for evolutionary matrix models with multiple traits, Journal of Mathematical Biology 75, No. 1 (2017), 491-520, DOI: 10.1007/s00285-016-1091-4
  13. P. De Leenheer, A. Mohapatra, H. A. Ohms, D. A. Lytle, and J. M. Cushing, The puzzle of partial migration: adaptive dynamics and evolutionary game theory perspectives, Journal of Theoretical Biology, 412 (2017), 172-185, DOI.org/10.1016/j.jtbi.2016.10.011
  14. A. Veprauskas and J. M. Cushing, A juvenile-adult population model: climate change, cannibalism, reproductive synchrony, and strong Allee effects, Journal of Biological Dynamics 11, Sup1 (2017), 1-24, DOI: 10.1080/17513758.2015.1131853
  15. J. M. Cushing and O. Diekmann, The many guises of R0 (a didactic note), Journal of Theoretical Biology 404 (2016), 295-302, DOI:10.1016/j.jtbi.2016.06.017
  16. E. P. Meissen, K. R. Salau, and J. M. Cushing, A global bifurcation theorem for Darwinian matrix models, Journal of Difference Equations and Applications 22, No. 8 (2016), 1114-1136, DOI 10.1080/10236198.2016.1177522
  17. J. M. Cushing, One dimensional maps as population and evolutionary dynamic models, Applied Analysis in Biological and Physical Sciences, Springer Proceedings in Mathematics & Statistics, Volume 186, (J. M. Cushing, M. Saleem, H. M. Srivastava, M. A. Khan, M. Merajuddin, eds.), Springer, India, 2016
  18. Shandelle Henson, J. M. Cushing and James Hayward, Modeling animal behavior in a changing environment, Resource Modeling Association Newsletter, Spring 2016
  19. A. Veprauskas and J. M. Cushing, Evolutionary dynamics of a multi-trait semelparous model, Discrete and Continuous Dynamical Systems Series B 21, No. 2 (2016), 655-676, DOI:10.3934/dcdsb.2016.21.655, errata
  20. A. S. Ackleh, J. M. Cushing, and P. L. Salceanu, On the dynamics of evolutionary competition models, Natural Resource Modeling 28, No. 4 (2015), 380-397, DOI: 10.1111/nrm.12074
  21. J. M. Cushing, S. M. Henson and J. L. Hayward, An evolutionary game theoretic model of cannibalism, Natural Resource Modeling 28, No. 4 (2015), 497-521, DOI: 10.1111/nrm.12079
  22. J. M. Cushing, The evolutionary dynamics of a population model with a strong Allee effect, Mathematical Biosciences and Engineering 12, No. 4 (2015), 643-660
  23. J. M. Cushing, On the Fundamental Bifurcation Theorem for Semelparous Leslie Models, in Dynamics, Games and Science (eds. J. P. Bourguignon, R. Jeltsch, A. Pinto, and M. Viana), CIM Mathematical Sciences Series, Springer, Berlin, (2015), 215-251
  24. J. M. Cushing, Backward bifurcations and strong Allee effects in matrix models for the dynamics of structured populations, Journal of Biological Dynamics 8 (2014), 57-73
  25. J. M. Cushing, An evolutionary Beverton-Holt model, Theory and Applications of Difference Equations and Discrete Dynamical Systems (Z. AlSharawi, J. M. Cushing, S. Elaydi, eds.), Springer Proceedings in Mathematics & Statistics, Vol. 102 (2014), Springer, Heidelberg, pp. 127-141
  26. J. M. Cushing and Simon Maccracken Stump, Darwinian dynamics of a juvenile-adult model, Mathematical Biosciences and Engineering 10, No. 4 (2013), 1017-1044
  27. J. M. Cushing and S. M. Henson, Stable bifurcations in nonlinear semelparous Leslie models, Journal of Biological Dynamics 6 (2012), 80-102
  28. S. L. Robertson, J. M. Cushing, and R. F. Costantino, Life stage: interactions and spatial patterns, Bulletin of Mathematical Biology 74 (2012), 491-508
  29. J. M. Cushing and Jarred Hudson, Evolutionary dynamics and strong Allee effects, Journal of Biological Dynamics 6, No. 2 (2012), 941-958
  30. J. M. Cushing, A dynamic dichotomy for a system of hierarchical difference equations, Journal of Difference Equations and Applications 18 No. 1 (2012), 1-2
  31. S. L. Robertson and J. M. Cushing, A bifurcation analysis of stage-structured density dependent integrodifference equations, Journal of Mathematical Analysis and Applications 388 (2012), 490-499
  32. J. M. Cushing, Difference equations, Encyclopedia of Theoretical Ecology, (A. Hastings and L. Gross, Editors-in-Chief), University of California Press, Berkeley, 2012
  33. J. M. Cushing and A. S. Ackleh, A net reproduction number for periodic matrix models, Journal of Biological Dynamics 6, No. 2 (2012), 166-188
  34. S. M. Henson, J. M. Cushing and J. L. Hayward, Socially-induced ovulation synchrony and its effect on seabird populations, Journal of Biological Dynamics 5, No. 5 (2011), 495-516
  35. S. L. Robertson and J. M. Cushing, Spatial segregation in stage-structured populations with an application to Tribolium, Journal of Biological Dynamics 5, No. 5 (2011), 398-409
  36. J. M. Cushing, On the relationship between r and R0 and its role in the bifurcation of equilibria of Darwinian matrix models, Journal of Biological Dynamics 5 (2011), 277-297
  37. R. C. Rael, T. L. Vincent and J. M. Cushing, Competitive outcomes changed by evolution (with errata), Journal of Biological Dynamics 5 (2011), 227-252
  38. S. M. Henson, J. L. Hayward, J. M. Cushing, and Joseph G. Galusha, Socially-induced synchronization of every-other-day egg laying in a seabird colony, The Auk 127, No. 3 (2010), 571-580
  39. J. M. Cushing, On the dynamics of a class of Darwinian matrix models, Nonlinear Dynamics and Systems Theory 10, No. 2 (2010), 103-116
  40. J. M. Cushing, A bifurcation theorem for Darwinian matrix models, Nonlinear Studies 17, No. 1 (2010), 1-13, errata
  41. J. M. Cushing, Matrix Models and Population Dynamics, a chapter in Mathematical Biology (Mark Lewis, A.J. Chaplain, James P. Keener, Philip K. Maini eds.), IAS/Park City Mathematics Series Vol 14, American Mathematical Society, Providence, RI, 2009, 47-150
  42. R. C. Rael, R. F. Costantino, J. M. Cushing, and T. L. Vincent, Using stage-structured evolutionary game theory to model the experimentally observed evolution of a genetic polymorphism, Evolutionary Ecology Research 11 (2009), 141-151
  43. J. M. Cushing, Three stage semelparous Leslie models, Journal of Mathematical Biology 59 (2009), 75-104
  44. S. L. Arpin and J. M. Cushing, Modeling frequency-dependent selection with an application to cichlid fish, Mathematical Biosciences and Engineering 5, No. 4 (2008), 889-903
  45. N. Chitnis, J. M. Hyman and J. M. Cushing, Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bulletin of Mathematical Biology 70 (2008), 1272-1296
  46. J. M. Cushing, S. M. Henson, C. C. Blackburn, Multiple mixed-type attractors in competition models, Journal of Biological Dynamics 1, No. 4 (2007), 347-362
  47. S. M. Henson, B. Dennis, J. L. Hayward, J. M. Cushing and J. G. Galusha, Predicting the dynamics of animal behavior in field populations, Animal Behavior 74, No. 1 (2007), 103-110
  48. R. C. Rael, T. L. Vincent, R. F. Costantino and J. M. Cushing, Evolution of corn oil sensitivity in the flour beetle, Advances in Dynamic Game Theory, Jorgensen, Quincampoix and Vincent, eds., Birkhäuser, Berlin, 2007, pp. 367-376
  49. S. M. Henson, J. G. Galusha, J. L. Hayward and J. M. Cushing, Modeling territory attendance and preening behavior in a seabird colony as functions of environmental conditions, Journal of Biological Dynamics 1, No. 1 (2007), 95-107
  50. J. M. Cushing, S. M. Henson and Lih-Ing Roeger, A competition model for species with juvenile-adult life cycle stages, Journal of Biological Dynamics 1, No. 2 (2007), 201-231
  51. J. M. Cushing, Nonlinearity and stochasticity in population dynamics, Mathematics for Ecology and Environmental Sciences, Volume 1, (Takeuchi, Iwasa, and Sato, eds.), Springer, Berlin, 2007
  52. N. Chitnis, J. M. Cushing and J. M. Hyman, Bifurcation analysis of a mathematical model for malaria transmission, SIAM Journal on Applied Mathematics 67, No. 1 (2006), 24-45
  53. J. M. Cushing, A juvenile-adult model with periodic vital rates, Journal of Mathematical Biology 53 (2006), 520-539
  54. R. A. Desharnais, R. F. Costantino, J. M. Cushing, S. M. Henson, B. Dennis and A. A. King, Experimental support of the scaling rule for demographic stochasticity, Ecological Letters 9 (2006), 537-547
  55. J. M. Cushing, Nonlinear semelparous Leslie models, Mathematical Biosciences and Engineering 3, No. 1 (2006), 17-36 (with ERRATA)
  56. J. M. Cushing and S. LeVarge, Some discrete competition models and the principle of competitive exclusion, Difference Equations and Discrete Dynamical Systems, Proceedings of the Ninth International Conference, (L. J. S. Allen, B. Aulbach, S. Elaydi, R. Sacker, editors), World Scientific, 2005 (ISBN 981-256-520-5), pp. 283-302
  57. R. F. Costantino, R. A. Desharnais, J. M. Cushing, B. Dennis, S. M. Henson and A. A. King, Nonlinear stochastic population dynamics: the flour beetle Tribolium as an effective tool of discovery, Advances in Ecological Research, Volume 37 (2005), 101-141
  58. S. R.-J. Jang and J. M. Cushing, Dynamics of hierarchical models in discrete-time, Journal of Difference Equations and Applications 11, No. 2 (2005), 95-116
  59. J. M. Cushing, S. Levarge, N. Chitnis, S. M. Henson, Some discrete competition models and the competitive exclusion principle, Journal of Difference Equations and Applications 10, No. 13-15 (2004), 1139-1151
  60. J. M. Cushing, The LPA model, Fields Institute Communications 43 (2004), 29-55
  61. J. M. Cushing, Population dynamics, in The Encyclopedia of Nonlinear Science, (A. Scott, editor) Routledge, Taylor and Francis Group, New York, 2004
  62. A. A. King, R. F. Costantino, J. M. Cushing, S. M. Henson, R. A. Desharnais and B. Dennis, Anatomy of a chaotic attractor: subtle model predicted patterns revealed in population data, Proceedings of the National Academy of Sciences 101, No. 1 (2003), 408-413
  63. S. M. Henson, A. A. King, R. F. Costantino, J. M. Cushing, B. Dennis, R. A. Desharnais, Explaining and predicting patterns in stochastic population systems, Proceedings of the Royal Society, London B 270 (2003), 1549-1553
  64. S. M. Henson, J. R. Reilly, S. L. Robertson, M. C. Schu, E. W. Davis and J. M. Cushing, Predicting irregularities in population cycles, SIAM Journal on Applied Dynamical Systems 2, No. 2 (2003), 238-253
  65. J. Edmunds, J. M. Cushing, R. F. Costantino, S. M. Henson, B. Dennis and R. A. Desharnais, Park's Tribolium competition experiments: a non-equilibrium species coexistence hypothesis, Journal of Animal Ecology 72 (2003), 703-712
  66. B. Dennis, R. A. Desharnais, J. M. Cushing, S. M. Henson and R. F. Costantino, Can noise induce chaos?, Oikos 102 (2003), 329-340
  67. J. M. Cushing, Cycle chains and the LPA model, Journal of Difference Equations and Applications 9, No. 7 (2003), 655-670
  68. S. R.-J. Jang and J. M. Cushing, A discrete hierarchical model of intra-specific competition, Journal of Mathematical Analysis and Applications 280 (2003), 102-122
  69. J. M. Cushing, S. M. Henson, A periodically forced Beverton-Holt equation, Journal of Difference Equations and Applications 8, No. 12 (2002), 1119-1120
  70. A. A. King, R. A. Desharnais, S. M. Henson, R. F. Costantino, J. M. Cushing and B. Dennis, Letter to editor: Random perturbations and lattice effects in chaotic population dynamics , Science 297 (27 September, 2002), 2163
  71. S. M. Henson, R. F. Costantino, J. M. Cushing, B. Dennis and R. A. Desharnais, Basins of attraction: population dynamics with two locally stable 4-cycles, Oikos 98 (2002), 17-24
  72. S. M. Henson, J. M. Cushing, Geometric transient solutions of autonomous scalar maps, Journal of Difference Equations and Applications 8 (2002), 61-73
  73. J. M. Cushing and S. M. Henson, Global dynamics of some periodically forced, monotone difference equations, Journal of Difference Equations and Applications 7 (2001), 859-872
  74. S. M. Henson, R. F. Costantino, J. M. Cushing, R. A. Desharnais, B. Dennis and A. A. King, Lattice effects observed in chaotic dynamics of experimental populations, Science 294 (19 Oct 2001), 602-605
  75. R. A. Desharnais, R. F. Costantino, J. M. Cushing, S. M. Henson and B. Dennis, Chaos and population control of insect outbreaks, Ecology Letters 4, No. 3 (2001), 229-235
  76. B. Dennis, R. A. Desharnais, J. M. Cushing, S. M. Henson and R. F. Costantino, Estimating chaos and complex dynamics in an insect population, Ecological Monographs 71, No. 2 (2001), 277-303
  77. J. M. Cushing, S. M. Henson, B. Dennis and R. A. Desharnais, R. F. Costantino and A. King, A chaotic attractor in ecology: theory and experimental data, Chaos, Solitons & Fractals 12, (2001), 219-234
  78. S. M. Henson, R. F. Costantino, J. M. Cushing, B. Dennis and R. A. Desharnais, Multiple attractors, saddles and population dynamics in periodic habitats, Bulletin of Mathematical Biology 61 (1999), 1121-1149
  79. J. M. Cushing, Global stability of some matrix equations in population dynamics, Journal of Difference Equations and Applications 5, No. 6 (1999), 557-560
  80. S. M. Henson, J. M. Cushing, R. F. Costantino, B. Dennis and R. A. Desharnais, Phase Switching in biological population, Proceedings of the Royal Society 265 (22 November 1998), 2229-2234
  81. Zhou Yicang and J.M. Cushing, Stability conditions for equilibria of nonlinear matrix population models, Journal of Difference Equations & Applications 4 (1998), 95-126
  82. J. M. Cushing, R. F. Costantino, B. Dennis, R. A. Desharnais and S. M. Henson, Nonlinear population dynamics: models, experiments, and data, Journal of Theoretical Biology 194, No. 1 (1998), 1-9
  83. J. M. Cushing, Periodically forced nonlinear systems of difference equations, Journal of Difference Equations and Applications 3 (1998), 547-561
  84. R. F. Costantino, J. M. Cushing, B. Dennis, R. A. Desharnais and S. M. Henson, Resonant population cycles in temporally fluctuating habitats, Bulletin of Mathematical Biology 60, No. 2 (1998), 247-275
  85. S. M. Henson and J. M. Cushing, The effect of periodic habitat fluctuations on a nonlinear insect population model, Journal of Mathemathical Biology 36 (1997), 201-226
  86. J. M. Cushing, B. Dennis, R. A. Desharnais and R. F. Costantino, Moving toward an unstable equilibrium: saddle nodes in population systems, Journal of Animal Ecology 67, No. 1 (1998), 298-306B. 
  87. Dennis, R. A. Desharnais, J. M. Cushing and R. F. Costantino, Transitions in population dynamics: equilibria to periodic cycles to aperiodic cycles, Journal of Animal Ecology 66 (1997), 704-729
  88. R. F. Costantino, R. A. Desharnais, J. M. Cushing and B. Dennis, Letter to the editor: Estimating chaos in an insect population, Science 276 (June 1997), 1881-1882
  89. J. M. Cushing, Nonlinear matrix equations and population dynamics, Chapter 6 in Structured Population Models in Marine, Terrestrial, and Freshwater Systems (Shripad Tuljapurkar and Hal Caswell, eds.), Population and Community Biology Series 18, Chapman and Hall, New York, 1997
  90. R. F. Costantino, R. A. Desharnais, J. M. Cushing and B. Dennis, Chaotic dynamics in an insect population, Science 275 (January 1997), 389-391
  91. J. M. Cushing, B. Dennis, R. A. Desharnais and R. F. Costantino, An interdisciplinary approach to understanding nonlinear ecological dynamics, Ecological Modelling 92 (1996), 111-119
  92. S. M. Henson and J. M. Cushing, Hierarchical models of intra-specific competition: scramble versus contest, Journal of Mathematical Biology (1996) 34, 755-772
  93. S. M. Henson and J. M. Cushing, Optimal parasitization in a size-structured host-parasitoid model, Nonlinear World 3 (1996), 1-18
  94. J. M. Cushing, Periodic cycles of nonlinear discrete renewal equations, Journal of Difference Equations & Applications 2 (1996), 117-137
  95. J. M. Cushing, Competition in hierarchically size-structured populations, Differential Equations and Applications to Biology and to Industry (Martelli, Cooke, Cumberbatch, Tang and Thieme, editors), World Scientific, Singapore, 1996 pp: 71-80
  96. Yang Kuang and J. M. Cushing, Global stability in a nonlinear difference-delay equation model of flour beetle population growth, Journal of Difference Equations and Applications 2 (1995), pp. 31-37
  97. J. M. Cushing, Systems of difference equations and structured population dynamics, Proceedings of the First International Conference on Difference Equations (Saber N. Elaydi, John R. Graef, Gerry Ladas, Allan C. Peterson, editors), Gordon and Breach Publishers, US, 1995, pp. 123-132
  98. B. Dennis, R. A. Desharnais, J. M. Cushing and R. F. Costantino, Nonlinear demographic dynamics: mathematical, models, statistical methods, and biological experiments, Ecological Monographs 65 (3), 1995, 261-281
  99. R. F. Costantino, J. M. Cushing, B. Dennis and R. A. Desharnais, Experimentally induced transitions in the dynamics behaviour of insect populations, Nature 375 (1995, May), 227-230
  100. J. M. Cushing and Jia Li, Oscillations caused by cannibalism in a size-structured population model, Canadian Applied Mathematics Quarterly 3 (1995), No. 2. 155-172
  101. J. M. Cushing, Nonlinear Matrix Models for Structured Population, Chapter 26 in Mathematical Population Dynamics III: Mathematical Methods and Modelling of Data, O. Arino, D. Axelrod, M. Kimmel, & M. Langlais, eds.,Wuerz Publishing Ltd, 1995
  102. J. M. Cushing, Structured Population Dynamics, Frontiers in Mathematical Biology, Lecture Notes in Biomathematics, Vol. 100, edited by S. A. Levin, Springer, Berlin, 1995, 280-295
  103. J. M. Cushing and Zhou Yicang, The net reproductive value and stability in structured population models, Natural Resource Modeling 8, No. 4 (1994), 1-37
  104. J. M. Cushing, Oscillations in age-structured population models with an Allee effect, Journal of Computational and Applied Mathematics 52, 1994, 71-80
  105. K. M. Crowe and J. M. Cushing, Optimal instar parasitization in a stage structured host-parasitoid model, Natural Resource Modeling 8, No. 2, 1994, 119-138
  106. J. M. Cushing, The dynamics of hierarchical age-structured populations, Journal of Mathematical Biology 32 (1994), 705-729
  107. J. M. Cushing, A size-structured model for cannibalism, Theoretical Population Biology 42 (1992), 347-361
  108. J. M. Cushing and Jia Li, Intra-specific competition and density dependent juvenile growth, Bulletin of Mathematical Biology 53, No. 4 (1992), 503-519
  109. J. M. Cushing, A discrete model of competing size-structured species, Theoretical Population Biology 41, No. 2 (1992), 372-387
  110. J. M. Cushing and Jia Li, The dynamics of a size-structured intraspecific competition model with density dependent juvenile growth rates, Chapter 6 in Individual Based Modeling: Concepts and Models, (D. DeAngelis and L.J. Gross, eds.), Routledge, Chapman and Hall, New York, 1992, 112-125
  111. J. M. Cushing, David Gay, Larry Grove, David Lomen and David Lovelock, The Arizona experience: software development & use, Proceedings of the Third International Conference on Techonology in Collegiate Mathematics, Addison-Wesley Publishing Company, 1992, 41-47
  112. J. M. Cushing, Some delay models for juvenile vs. adult competition, Differential Equations & Applications in Biology and Population Dynamics (Busenberg & Martelli, editors), Springer, 1991, 177-188
  113. J. M. Cushing, A simple model of cannibalism, Mathematical Biosciences 107, No.1, (1991), 47-72
  114. J. M. Cushing and Jia Li, Juvenile versus adult competition, Journal of Mathematical Biology 29 (1991), 457-473
  115. J. M. Cushing, Competing size-structured species, Mathematical Population Dynamics (Chapter 3, p. 27-44), O. Arino, D.E. Axelrod and M. Kimmel eds., Marcel Dekker, Inc., NY 1991
  116. J. M. Cushing, Some competition models for size-structured populations, Rocky Mountain Journal of Mathematics 20, No. 4 (1990), 879-897
  117. J. M. Cushing, A strong ergodic theorem for some nonlinear matrix models for structured population growth, Natural Resource Modeling 3, No. 3 (1989), 331-357
  118. J. M. Cushing and Jia Li, On Ebenman's model for the dynamics of a population with competing juveniles and adults, Bulletin of Mathematical Biology 51, No. 6, (1989), 687-713
  119. J. M. Cushing, A competition model for size-structured species, SIAM Journal of Applied Mathematics 49, No. 3 (1989), 838-858
  120. J. M. Cushing, The Allee effect in age-structured population dynamics, Mathematical Ecology (S.A. Levin & T. Hallam, editors), World Scientific, New Jersey, 1988, 479-505
  121. J. M. Cushing, Nonlinear matrix models and population dynamics, Natural Resource Modeling 2, No. 4 (1988), 539-580
  122. J. M. Cushing, Equilibria and oscillations in age-structured population growth models, Mathematical Modelling of Environmental and Ecological Systems (edited by J. B. Shukla, T.G. Hallam, & V. Capasso), Elsevier Science Publishers, NY, 1987, 153-175
  123. J. M. Cushing, Equilibria in systems of interacting structured populations, Journal of Mathematical Biology 24 (1987), 627-649
  124. J. M. Cushing, Oscillatory population growth in periodic environments, Theoretical Population Biology 30, no 3 (1986), 289-308
  125. J. M. Cushing, Periodic McKendrick equations for age-structured population growth, Computers and Mathematics with Applications 12A, No. 45 (1986), 513-526 (Reprinted in Advances in Hyperbolic Differential Equations Vol. 3 , edited by M. Witten, Pergamon Press, 1986)
  126. J. M. Cushing, Periodic Lotka-Volterra competition equations, Journal of Mathematical Biology 24 (1986), 381-403
  127. J. M. Cushing, Equilibria in structured populations, Journal of Mathematical Biology 23, No. 1 (1985), 15-39
  128. J. M. Cushing, Global branches of equilibrium solutions of the McKendrick equations for age-structured population growth, Computers and mathematics with Applications 11 (1985), 175-188 (Reprinted in Advances in Hyperbolic Differential Equations Vol. 2 , edited by M. Witten, Pergamon Press, 1985)
  129. J. M. Cushing, Equilibrium solutions of general age-structured population growth equations, Mathematical Models of Renewable Resources 3 (1985), 104-108
  130. J. M. Cushing, Periodic McKendrick equations, Proceedings of the IMACS World Congress, Olso, Norway, 1985
  131. J. M. Cushing, Existence and stability of equilibria in age-structured population dynamics, Journal of Mathematical Biology 20, No. 3 (1984), 259-276
  132. J. M. Cushing, Periodic two-predator, one-prey interactions and the time sharing of a resource niche, SIAM Journal of Applied Mathematics 44, No. 2 (1984), 392-410
  133. J. M. Cushing and M. Saleem, A competition model with age-structure, Lecture Notes in Biomathematics 54, Springer, New York, 1984,178-192
  134. J. M. Cushing, Bifurcation of time periodic solutions of the McKendrick equations with applications to population dynamics, Computers and Mathematics with Applications 9, No. 3 (1983), 459-478 (Reprinted in Advances in Hyperbolic Differential Equations, Volume 1, edited by M. Witten, Pergamon Press, 1983)
  135. J. M. Cushing, Periodic Lotka-Volterra systems and time sharing of ecological niches, Lecture Notes in Biomathematics 52, pp 342-348, Springer, New York, 1983
  136. J. M. Cushing and M. Saleem, A predator-prey model with age structure, Journal of Mathematical Biology 14 (1982), 231-250
  137. J. M. Cushing, Periodic Kolmogorov systems, SIAM Journal of Mathematical Analysis 13, No. 5 (1982), 811-827
  138. J. M. Cushing, Bifurcation of periodic solutions of nonlinear equations in age-structured population dynamics, Nonlinear Phenomena in Mathematical Sciences (V. Lakshmikantham, Ed.), 279-288 Academic Press, 1982, 279-288
  139. J. M. Cushing, Stability and maturation periods in age-structured populations, Differential Equations and Applications in Ecology, Epidemics and Population Dynamics (Busenberg and Cooke, editors), 163-182, Academic Press, NY, 1981
  140. J. M. Cushing and S. D. Simmes, Bifurcation of asymptotically periodic solutions of Volterra integral equations, Journal of Integral Equations 4 (1980), 339-361
  141. J. M. Cushing, Model stability and instability in age structured populations, Journal of Theoretical Biology 86 (1980), 709-730
  142. J. M. Cushing, Two species competition in a periodic environment, Journal of Mathematical Biology 10 (1980), 385-400
  143. J. M. Cushing, Stability and instability in predator-prey models with growth rate response delays, Rocky Mountain Journal of Mathematics 9, No. 1 (1979), 43-50
  144. J. M. Cushing, Nontrivial periodic solutions of integrodifferential equations, Journal of Integral Equations 1, No. 2 (1979), 165-181
  145. J. M. Cushing, Nontrivial periodic solutions of some Volterra integral equations, Lecture Notes in Mathematics, Vol. 737, Springer, New York, 1979, 50-66, DOI:10.1007/BFb0064495
  146. J. M. Cushing, Volterra Integrodifferential Equations in Population Dynamics, Mathematics of Biology (M. Iannelli, editor), Proc. 1979 C.I.M.E. Summer School, Florence, Italy, ISBN 978-3-642-11069-6, Springer-Verlag, Berline Heidelberg 2010
  147. J. M. Cushing, Bifurcation of periodic oscillations due to delays in single species growth models, Journal of Mathematical Biology 6 (1978), 145-161
  148. J. M. Cushing, Strongly admissible operators and Banach space solutions of nonlinear equations, Funkcialaj Ekvacioj 20, No. 3 (1977), 237-245
  149. J. M. Cushing, On the oscillatory nature of general predator-prey models with delays, Journal of Nonlinear Analysis 1, No. 6 (1977), 583-592
  150. J. M. Cushing, Bifurcation of periodic solutions of integro-differential equations with applications to time delay models in population dynamics, SIAM Journal of Applied Mathematics 33, No. 4 (1977), 640-654
  151. J. M. Cushing, Stable positive periodic solutions of the time dependent logistic equation under possible hereditary influences, Journal of Mathematical Analysis and Applications 3 (1977), 747-754
  152. J. M. Cushing, Time delays in single species growth models, Journal of Mathematical Biology 3 (1977), 257-264
  153. J. M. Cushing, Periodic time-dependent predator-prey systems, SIAM Journal of Applied Mathematics 32, No. 1 (1977), 82-95
  154. J. M. Cushing, Time delays in predator-prey systems, Nonlinear Systems and Applications (V. Lakshmikantham, ed.), 469-472, Academic Press, New York, 1977
  155. J. M. Cushing, Admissible operators and solutions of perturbed operator equations, Funkcialaj Ekvacioj 19 (1976), 79-84
  156. J. M. Cushing, Bounded solutions of perturbed Volterra integro-differential systems, Journal of Differential Equations 20, No.1 (1976), 61-70
  157. J. M. Bownds, J. M. Cushing and R. Schutte, Existence, uniqueness and extendability of solutions of Volterra integral equations with multiple, variable lags, Funkcialaj Ekvacioj 19 (1976), 101-111
  158. J. M. Cushing, Extremal tests for functions of several real variables at degenerate critical points, Aequationes Mathematicae 13 (1976), 89-96
  159. J. M. Cushing, Forced asymptotically periodic solutions of predator-prey systems with or without hereditary effects, SIAM Journal of Applied Mathematics 30, No. 4 (1976), 665-674
  160. J. M. Cushing, Periodic solutions of two species interaction models with lags, Mathematical Biosciences 31 (1976), 143-156
  161. J. M. Cushing, Periodic solutions of Volterra's population equation with hereditary effects, SIAM Journal of Applied Mathematics 31, No. 2 (1976), 251-260 (Erratum, SIAM Journal of Applied Mathematics 32, No. 2 (1977), 895)
  162. J. M. Cushing, Predator-prey interactions with time delays, Journal of Mathematical Biology 3 (1976), 369-380
  163. J. M. Cushing, Stable limit cycles of time dependent multi-species interactions, Mathematical Biosciences 31 (1976), 259-273
  164. J. M. Bownds and J. M. Cushing, On preserving stability of Volterra integral equations under a general class of perturbations, Mathematical Systems Theory 9, No. 2 (1975), 117-131
  165. J. M. Bownds and J. M. Cushing, On the behavior of solutions of predator-prey equations with hereditary terms, Mathematical Biosciences 26 (1975), 41-54
  166. J. M. Cushing, An operator equation and bounded solutions of integro-differential systems, SIAM Journal of Mathematical Analysis 6, No. 3 (1975), 433-445
  167. J. M. Bownds and J. M. Cushing, Some stability theorems for systems of Volterra integral equations, Applicable Analysis 5 (1975), 65-78
  168. J. M. Cushing, Stability of perturbed Volterra integral equations, Journal of Mathematical Analysis and Applications 50, No. 2 (1975), 325-340
  169. J. M. Cushing, Nonlinear Steklov problems on nonsymmetric domains, Journal of Mathematical Analysis and Applications 43 (1973), 743-753
  170. J. M. Bownds and J. M. Cushing, On strong stability for linear integral equations, Mathematical Systems Theory 7, No. 3 (l973), 193-200
  171. J. M. Bownds and J. M. Cushing, A representation formula for linear Volterra integral equations, Bulletin of the American Mathematics Society 79, No. 3 (1973), 532-536
  172. J. M. Bownds and J. M. Cushing, Strong stability of perturbed systems of Volterra integral equations, Mathematical Systems Theory 7, No. 4 (1973), 360-366
  173. J. M. Cushing, Nonlinear Steklov problems on the unit circle II (and a hydrodynamical applications), Journal of Mathematical Analysis and Applications 39, No. 2 (1972), 267-278
  174. J. M. Cushing, Nonlinear Steklov problems on the unit circle I, Journal of Mathematical Analysis and Applications 38, No. 3 (1972), 766-783
  175. J. M. Bownds and J. M. Cushing, Some stability criteria for linear systems of Volterra integral equations, Funkcialaj Ekvacioj 15, No. 2 (1972), 101-117
  176. J. M. Cushing, Some existence results for Nonlinear Steklov problems, Lecture Notes in Mathematics, Vol. 280, 236-240, Springer, New York, 1972
  177. J. M. Cushing, Global branches of solutions to nonlinear elliptic eigenvalue problems, Indiana University Mathematics Journal 20, No. 11 (1971), 1035-1045
  178. J. M. Cushing, Some existence theorems for nonlinear eigenvalue problems associated with elliptic equations, Archive of Rational Mechanics and Analysis 42, No. 1 (1971), 63-76
  179. J. M. Cushing, A uniqueness criterion for harmonic functions under nonlinear boundary conditions, Journal of Mathematical Analysis and Applications 33, No. 2 (1971), 443-448
  180. J. M. Cushing, Uniqueness of positive solutions to nonlinear elliptic equations, SIAM Journal of Mathematical Analysis 2, No. 2 (1971), 290-292
  181. J. M. Cushing and D. R. Dunninger, Uniqueness theorems under nonlinear boundary conditions for some quasi-linear elliptic equations, Journal of Mathematical Analysis and Applications 33, No. 3 (l971), 114-127
  182. J. M. Cushing, Local uniqueness for harmonic functions under nonlinear boundary conditions, Journal of Differential Equations 8, No. 3 (1970), 512-522
  183. J. M. Cushing, On a conjecture of Levi-Civita, Journal of Mathematics and Mechanics 19, No. 12, (1970), 1047-1050, http://www.jstor.org/stable/24901654
  184. J. M. Cushing, Uniqueness and comparison of harmonic functions under nonlinear boundary conditions, Journal of Mathematical Analysis and Applications 28, No. 3 (1969), 581-589

J. M. Cushing / Department of Mathematics / Program in Applied Mathematics / University of Arizona / Tucson, AZ 85721-0089
(revised 11 April 2025)
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