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PUBLICATIONS

J. M. Cushing
Professor
Department of Mathematics
Program in Applied Mathematics
University of Arizona
Tucson, AZ  85721
USA
 

BOOKS



1. Chaos in Ecology: Experimental Nonlinear Dynamics, Theoretical Ecology Series, Vol. 1, Academic Press (Elsevier Science), New York, 2003, ISBN: 0-12-1988767  (jointly with R. F. Costantino, B. Dennis, R. A. Desharnais, S. M. Henson)

 “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)



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

3.  Differential Equations: An Applied Approach, Pearson - Prentice Hall, Upper Saddle river, New Jersey 2004, ISBN: 0-13-044930-X

4. Integrodifferential Equations and Delay Models in Population Dynamics, Lecture Notes in Biomathematics 20, Springer, Berlin Heidelberg New York, 1977, ISBN 3-540-08449-5  &  ISBN 0-387-08449-5





JOURNAL ARTICLES & BOOK CHAPTERS

In Press
  1. S. L. Robertson, J. M. Cushing and R. F. Costantino, Life stage: interactions and spatial patterns, Bulletin of Mathematical Biology
  2. J. M. Cushing, Difference Equations, Sourcebook in Theoretical Ecology, (A. Hastings and L. Gross, Editors-in-Chief), University of California Press 
Published
  1. J. M. Cushing, A dynamic dichotomy for a system of hierarchical difference equations, Journal of Difference Equations and Applications, DOI:10.1080/10236198.2011.628319
  2. 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
  3. 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
  4. 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
  5. J. M. Cushing and A. S. Ackleh, A net reproduction number for periodic matrix models, Journal of Biological Dynamics, DOI:10.108-/17513758.2010.54410
  6. 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
  7. C. Rael, T. L. Vincent and J. M. Cushing, Competitive outcomes changed by evolution, Journal of Biological Dynamics 5 (2011), 227-252
  8. 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
  9. J. M. Cushing, On the dynamics of a class of Darwinian matrix models, Nonlinear Dynamics and Systems Theory 10, No. 2 (2010), 103-116
  10. J. M. Cushing, A bifurcation theorem for Darwinian matrix models, Nonlinear Studies 17, No. 1 (2010), 1-13
  11. 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
  12. 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
  13. J. M. Cushing, Three stage semelparous Leslie models, Journal of Mathematical Biology 59 (2009), 75-104  JMB reprint
  14. 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
  15. 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
  16. 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
  17. 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
  18. 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, Jørgensen, Quincampoix and Vincent, eds., Birkhäuser, Berlin, 2007, pp. 367-376
  19. 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
  20. 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
  21. 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
  22. J. M. Cushing, A juvenile-adult model with periodic vital rates, Journal of  Mathematical Biology 53 (2006), 520-539
  23. J. M. Cushing, Nonlinearity and stochasticity in population dynamics, Mathematics for Ecology and Environmental Sciences, Volume 1, Springer, Berlin, 2006
  24. 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
  25. J. M. Cushing, Nonlinear semelparous Leslie models, Mathematical Biosciences and Engineering 3, No. 1 (2006), 17-36
  26. 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
  27. R. F. Costantino, R. A. Desharnais, J. M. Cushing, B. Dennis, S. M. Henson and A. A. King, The flour beetle Tribolium as an effective tool of discovery, Advances in Ecological Research, Volume 37, 2005
  28. 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
  29. 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
  30. J. M. Cushing, The LPA model, Fields Institute Communications 43 (2004), 29-55
  31. J. M. Cushing, Population dynamics, in The Encyclopedia of Nonlinear Science, (A. Scott, editor) Routledge, Taylor and Francis Group, New York, 2004
  32. 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
  33. 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
  34. 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
  35. 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
  36. B. Dennis, R. A. Desharnais, J. M. Cushing, S. M. Henson and R. F. Costantino, Can noise induce chaos?, Oikos 102 (2003), 329-340
  37. J. M. Cushing, Cycle chains and the LPA model, Journal of Difference Equations and Applications 9, No. 7 (2003), 655-670
  38. 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
  39. J. M. Cushing, S. M. Henson, A periodically forced Beverton-Holt equation, Journal of Difference Equations and Applications 8, No. 12 (2002), 1119-1120
  40. 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
  41. 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
  42. S. M. Henson, J. M. Cushing, Geometric transient solutions of autonomous scalar maps, Journal of Difference Equations and Applications 8 (2002), 61-73
  43. 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
  44. 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 
  45. 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
  46. 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
  47. 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
  48. 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
  49. J. M. Cushing, Global stability of some matrix equations in population dynamics, Journal of Difference Equations and Applications 5, No. 6 (1999), 557-560
  50. 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
  51. Zhou Yicang and  J.M. Cushing, Stability conditions for equilibria of nonlinear matrix population models, Journal of Difference Equations & Applications 4 (1998), 95-126
  52. 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
  53. J. M. Cushing, Periodically forced nonlinear systems of difference equations, Journal of Difference Equations and Applications 3 (1998), 547-561
  54. 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
  55. 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
  56. 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)
  57. B. 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
  58. 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
  59. 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
  60. R. F. Costantino, R. A. Desharnais, J. M. Cushing and B. Dennis, Chaotic dynamics in an insect population, Science 275 (January 1997), 389-391
  61. 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
  62. S. M. Henson and J. M. Cushing, Hierarchical models of intra-specific competition: scramble versus contest, Journal of Mathematical Biology (1996) 34, 755-772
  63. S. M. Henson and J. M. Cushing, Optimal parasitization in a size-structured host-parasitoid model, Nonlinear World 3 (1996), 1-18
  64. J. M. Cushing, Periodic cycles of nonlinear discrete renewal equations, Journal of Difference Equations & Applications 2 (1996), 117-137
  65. 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
  66. 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
  67. 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
  68. 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, pp. 261-281
  69. 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
  70. J. M. Cushing and Jia Li, Oscillations caused by cannibalism in a size-structured population model, Canadian Applied Mathematics Quarterly 3 (1995), No. 2,
  71. J. M. Cushing, Nonlinear Matrix Models for Structured Population, chapter 6 in Mathematical Population Dynamics III: Mathematical Methods and Modelling of Data, O. Arino, D. Axelrod, M. Kimmel, & M. Langlais, eds.,Wuerz Publishing Ltd, 1995, Chapter 26
  72. 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
  73. 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
  74. J. M. Cushing, Oscillations in age-structured population models with an Allee effect, Journal of Computational and Applied Mathematics 52, 1994, 71-80
  75. 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
  76. J. M. Cushing, The dynamics of hierarchical age-structured populations, Journal of Mathematical Biology 32 (1994), 705-729
  77. J. M. Cushing, A size-structured model for cannibalism, Theoretical Population Biology 42 (1992), 347-361
  78. J. M. Cushing and Jia Li, Intra-specific competition and density dependent juvenile growth, Bulletin of Mathematical Biology 53, No. 4 (1992), 503-519
  79. J. M. Cushing, A discrete model of competing size-structured species, Theoretical Population Biology 41, No. 2 (1992), 372-387
  80. 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
  81. 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
  82. J. M. Cushing, A simple model of cannibalism, Mathematical Biosciences 107, No.1, (1991), 47-72
  83. J. M. Cushing and Jia Li, Juvenile versus adult competition, Journal of Mathematical Biology 29 (1991), 457-473
  84. 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
  85. J. M. Cushing, David Gay, Larry Grove, David Lomen and David Lovelock, The Arizona experience: software development & use, Proceedings of the International Conference on Techonology in Collegiate Mathematics, 1991
  86. J. M. Cushing, Some competition models for size-structured populations, Rocky Mountain Journal of Mathematics 20, No. 4 (1990), 879-897
  87. 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
  88. 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
  89. J. M. Cushing, A competition model for size-structured species, SIAM Journal of Applied Mathematics 49, No. 3 (1989), 838-858
  90. J. M. Cushing, The Allee effect in age-structured population dynamics, Mathematical Ecology (S.A. Levin & T. Hallam, editors), World Scientific, New Jersey, 1988, pp 479-505
  91. J. M. Cushing, Nonlinear matrix models and population dynamics, Natural Resource Modeling 2, No. 4 (1988), 539-580
  92. 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
  93. J. M. Cushing, Equilibria in systems of interacting structured populations, Journal of Mathematical Biology 24 (1987), 627-649
  94. J. M. Cushing, Oscillatory population growth in periodic environments, Theoretical Population Biology 30, no 3 (1986), 289-308
  95. 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)
  96. J. M. Cushing, Periodic Lotka-Volterra competition equations, Journal of Mathematical Biology 24 (1986), 381-403
  97. J. M. Cushing, Equilibria in structured populations, Journal of Mathematical Biology 23, No. 1 (1985), 15-39
  98. 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)
  99. J. M. Cushing, Equilibrium solutions of general age-structured population growth equations, Mathematical Models of Renewable Resources 3 (1985), 104-108
  100. J. M. Cushing, Periodic McKendrick equations, Proceedings of the IMACS World Congress, Olso, Norway, 1985
  101. J. M. Cushing, Existence and stability of equilibria in age-structured population dynamics, Journal of Mathematical Biology 20, No. 3 (1984), 259-276
  102. 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
  103. J. M. Cushing and M. Saleem, A competition model with age-structure, Lecture Notes in Biomathematics 54, Springer, New York, 1984,178-192
  104. 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)
  105. J. M. Cushing and M. Saleem, Competition and age-structure, Lecture Notes in Biomathematics (Mathematical Ecology) 54, pp 178-192, Springer, New York, 1983
  106. 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
  107. J. M. Cushing and M. Saleem, A predator-prey model with age structure, Journal of Mathematical Biology 14 (1982), 231-250
  108. J. M. Cushing, Periodic Kolmogorov systems, SIAM Journal of Mathematical Analysis 13, No. 5 (1982), 811-827
  109. 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 45
  110. J. M. Cushing, Stability versus delays caused by 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
  111. J. M. Cushing and S. D. Simmes, Bifurcation of asymptotically periodic solutions of Volterra integral equations, Journal of Integral Equations 4 (1980), 339-361
  112. J. M. Cushing, Model stability and instability in age structured populations, Journal of Theoretical Biology 86 (1980), 709-730
  113. J. M. Cushing, Two species competition in a periodic environment, Journal of Mathematical Biology 10 (1980), 385-400
  114. 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
  115. J. M. Cushing, Nontrivial periodic solutions of integrodifferential equations, Journal of Integral Equations 1 (1979), 165-181
  116. J. M. Cushing, Bifurcation of periodic solutions of Volterra integral equations, Lecture Notes in Mathematics, Vol. 737, 50-66, Springer, New York, 1979
  117. J. M. Cushing, Lectures on Integrodifferential Equations in Population Dynamics, Proc. CIME Session on Mathematics in Biology II, Ciclo 1979, Florence, Italy
  118. J. M. Cushing, Bifurcation of periodic oscillations due to delays in single species growth models, Journal of Mathematical Biology 6 (1978), 145-161
  119. J. M. Cushing, Strongly admissible operators and Banach space solutions of nonlinear equations, Funkcialaj Ekvacioj 20, No. 3 (1977), 237-245
  120. J. M. Cushing, On the oscillatory nature of general predator-prey models with delays, Journal of Nonlinear Analysis 1, No. 6 (l977), 583-592
  121. 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
  122. J. M. Cushing, Stable positive periodic solutions of the time dependent logistic equation under possible hereditary influences, Journal of Mathematical Analysis and Applications 3 (l977), 747-754
  123. J. M. Cushing, Time delays in single species growth models, Journal of Mathematical Biology 3 (l977), 257-264
  124. J. M. Cushing, Periodic solutions of time dependent predator-prey systems, SIAM Journal of Applied Mathematics 32, No. 1 (l977), 82-95
  125. J. M. Cushing, Time delays in predator-prey systems, Nonlinear Systems and Applications (V. Lakshmikantham, ed.), 469-472, Academic Press, New York, 1977
  126. J. M. Cushing, Admissible operators and solutions of perturbed operator equations, Funkcialaj Ekvacioj 19 (1976), 79-84
  127. J. M. Cushing, Bounded solutions of perturbed Volterra integro-differential systems, Journal of Differential Equations 20, No.1 (1976), 61-70
  128. 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
  129. J. M. Cushing, Extremal tests for functions of several real variables at degenerate critical points, Aequationes Mathematicae 13 (1976), 89-96
  130. 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
  131. J. M. Cushing, Periodic solutions of two species interaction models with lags, Mathematical Biosciences 31 (1976), 143-156
  132. 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)
  133. J. M. Cushing, Predator-prey interactions with time delays, Journal of Mathematical Biology 3 (1976), 369-380
  134. J. M. Cushing, Stable limit cycles of time dependent multi-species interactions, Mathematical Biosciences 31 (1976), 259-273
  135. 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
  136. 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
  137. J. M. Cushing, An operator equation and bounded solutions of integro-differential systems, SIAM Journal of Mathematical Analysis 6, No. 3 (1975), 433-445
  138. J. M. Bownds and J. M. Cushing, Some stability theorems for systems of Volterra integral equations, Applicable Analysis 5 (1975), 65-78
  139. J. M. Cushing, Stability of perturbed Volterra integral equations, Journal of Mathematical Analysis and Applications 50, No. 2 (1975), 325-340
  140. J. M. Cushing, Nonlinear Steklov problems on nonsymmetric domains, Journal of Mathematical Analysis and Applications 43 (1973), 743-753
  141. J. M. Bownds and J. M. Cushing, On strong stability for linear integral equations, Mathematical Systems Theory 7, No. 3 (l973), 193-200
  142. 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
  143. 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
  144. 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
  145. J. M. Cushing, Nonlinear Steklov problems on the unit circle I, Journal of Mathematical Analysis and Applications 38, No. 3 (1972), 766-783
  146. 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
  147. J. M. Cushing, Some existence results for Nonlinear Steklov problems, Lecture Notes in Mathematics, Vol. 280, 236-240, Springer, New York, 1972
  148. J. M. Cushing, Global branches of solutions to nonlinear elliptic eigenvalue problems, Indiana University Mathematics Journal 20, No. 11 (1971), 1035-1045
  149. Some existence theorems for nonlinear eigenvalue problems associated with elliptic equations, Archive of Rational Mechanics and Analysis 42, No. 1 (1971), 63-76
  150. 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
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J. M. Cushing  / Department of Mathematics  / Program in Applied Mathematics  / University of Arizona / Tucson, AZ 85721-0089
 (revised 8 February 2012)
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