1. 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
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
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
- Shandelle M. Henson, Robert A. Desharnais, R. F. Costantino, J. M. Cushing, and Brian Dennis, Nonlinear Patterns in Population Dynamics: Theory and Experiments, Chapman & Hall/CRC, to appear 2025
BOOKS
EDITED
- Sorin Olaru, Jim. Cushing, Saber Elaydi, 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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] ©2020, pp. 231–243, DOI
10.1007/978-3-030-60107-2_10. MR4219152
- 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.
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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.
- Shandelle Henson, J. M.
Cushing and
James Hayward, Modeling
animal behavior in a changing environment, Resource Modeling Association
Newsletter,
Spring 2016
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- J.
M. Cushing and Simon Maccracken
Stump, Darwinian
dynamics of a juvenile-adult model,
Mathematical Biosciences and
Engineering 10, No. 4 (2013),
1017-1044
- J.
M. Cushing and S. M. Henson, Stable
bifurcations in nonlinear semelparous Leslie models, Journal
of Biological Dynamics
6
(2012), 80-102
- S.
L. Robertson, J. M. Cushing, and R.
F. Costantino, Life
stage: interactions and spatial patterns, Bulletin
of Mathematical Biology 74
(2012), 491-508
- J.
M. Cushing and Jarred Hudson, Evolutionary
dynamics and strong Allee effects, Journal of Biological
Dynamics
6,
No. 2 (2012), 941-958
- J.
M. Cushing, A
dynamic dichotomy for a system of hierarchical difference equations,
Journal
of Difference Equations
and Applications 18 No. 1
(2012), 1-26
- 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
- J. M.
Cushing, Difference
equations,
Encyclopedia of
Theoretical Ecology, (A.
Hastings and L. Gross, Editors-in-Chief), University of California
Press, Berkeley, 2012
- 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
- 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
- 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
- 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
- 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
- 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
- J. M.
Cushing, On
the
dynamics
of
a
class
of
Darwinian matrix models, Nonlinear
Dynamics and Systems Theory
10, No. 2 (2010), 103-116
- J.
M. Cushing, A
bifurcation theorem for Darwinian matrix models, Nonlinear
Studies 17, No. 1 (2010), 1-13
, errata
- 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
- 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
- J.
M. Cushing, Three
stage
semelparous Leslie models,
Journal
of Mathematical Biology
59 (2009), 75-104
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- J.
M. Cushing, A
juvenile-adult model with periodic vital rates, Journal
of Mathematical Biology
53 (2006), 520-539
- 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
- J.
M. Cushing, Nonlinear
semelparous
Leslie models, Mathematical
Biosciences and Engineering
3, No. 1 (2006), 17-36 (with ERRATA)
- 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
- 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
- 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
- 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
- J.
M. Cushing, The
LPA model, Fields
Institute Communications 43
(2004), 29-55
- J.
M. Cushing, Population dynamics, in The
Encyclopedia
of Nonlinear Science, (A. Scott,
editor) Routledge, Taylor and
Francis Group, New York, 2004
- 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
- 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
- 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
- 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
- B.
Dennis, R. A. Desharnais, J. M.
Cushing, S. M. Henson and R. F. Costantino, Can
noise induce chaos?, Oikos 102
(2003), 329-340
- J.
M. Cushing, Cycle
chains and the LPA
model, Journal
of Difference
Equations and Applications 9,
No. 7 (2003), 655-670
- 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
- J.
M. Cushing, S. M. Henson, A
periodically forced
Beverton-Holt equation, Journal
of Difference Equations and Applications
8, No. 12 (2002),
1119-1120
- 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
- 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
- S.
M. Henson, J. M. Cushing, Geometric
transient solutions of autonomous scalar maps, Journal
of Difference Equations and
Applications 8 (2002), 61-73
- 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
- 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
- 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
- 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
- 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
- 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
- J.
M. Cushing, Global
stability of
some matrix equations in population dynamics, Journal
of Difference Equations and
Applications 5, No. 6
(1999), 557-560
- 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
- Zhou
Yicang and J.M. Cushing, Stability
conditions
for
equilibria
of
nonlinear
matrix
population models, Journal
of
Difference Equations & Applications
4 (1998), 95-126
- 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
- J.
M. Cushing, Periodically
forced nonlinear systems of difference equations, Journal
of Difference Equations and
Applications 3 (1998),
547-561
- 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
- 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
- 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), 298-306
- 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
- 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
- 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
- R.
F. Costantino, R. A. Desharnais, J.
M. Cushing and B. Dennis, Chaotic
dynamics
in an insect population, Science
275 (January 1997), 389-391
- 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
- S.
M. Henson and J. M. Cushing, Hierarchical
models of
intra-specific competition: scramble versus contest, Journal
of Mathematical Biology
(1996) 34, 755-772
- S.
M. Henson and J. M. Cushing, Optimal
parasitization in a size-structured host-parasitoid model, Nonlinear
World 3 (1996), 1-18
- J.
M. Cushing, Periodic
cycles of
nonlinear discrete renewal equations, Journal
of Difference Equations &
Applications 2 (1996),
117-137
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- J.
M. Cushing, Oscillations
in
age-structured population models with an Allee effect, Journal
of Computational and Applied
Mathematics 52, 1994, 71-80
- 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
- J.
M. Cushing, The
dynamics of hierarchical age-structured populations, Journal
of Mathematical Biology 32
(1994), 705-729
- J.
M. Cushing, A
size-structured
model for cannibalism, Theoretical
Population Biology 42 (1992),
347-361
- J.
M. Cushing and Jia Li, Intra-specific
competition
and density dependent juvenile growth, Bulletin
of Mathematical Biology
53, No. 4 (1992), 503-519
- J.
M. Cushing, A
discrete model of competing size-structured species, Theoretical
Population Biology 41,
No. 2 (1992), 372-387
- 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
- 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
- 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
- J.
M. Cushing, A
simple model of
cannibalism, Mathematical
Biosciences 107, No.1,
(1991), 47-72
- J.
M. Cushing and Jia Li, Juvenile
versus
adult competition, Journal
of
Mathematical Biology 29
(1991), 457-473
- 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
- J.
M. Cushing, Some
competition models for
size-structured populations,
Rocky Mountain Journal of Mathematics
20, No. 4 (1990), 879-897
- 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
- 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
- J.
M. Cushing, A
competition model
for size-structured species, SIAM
Journal of Applied Mathematics
49, No. 3 (1989), 838-858
- 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
- J.
M. Cushing, Nonlinear matrix models
and population dynamics, Natural
Resource Modeling 2, No. 4
(1988), 539-580
- 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
- J.
M. Cushing, Equilibria
in systems of interacting structured populations, Journal
of Mathematical Biology 24
(1987), 627-649
- J.
M. Cushing, Oscillatory
population
growth in periodic environments, Theoretical
Population Biology 30, no 3
(1986), 289-308
- 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)
- J.
M. Cushing, Periodic
Lotka-Volterra
competition equations, Journal
of Mathematical Biology 24
(1986), 381-403
- J.
M. Cushing, Equilibria
in
structured populations, Journal
of Mathematical Biology 23,
No. 1 (1985), 15-39
- 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)
- J.
M. Cushing, Equilibrium solutions of
general age-structured population growth equations, Mathematical Models of
Renewable Resources
3 (1985), 104-108
- J.
M. Cushing, Periodic McKendrick
equations, Proceedings
of the IMACS
World Congress, Olso, Norway,
1985
- J.
M. Cushing, Existence
and
stability of equilibria in age-structured population dynamics, Journal
of Mathematical Biology 20,
No. 3 (1984), 259-276
- 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
- J.
M. Cushing and M. Saleem, A
competition model with age-structure, Lecture
Notes in Biomathematics 54,
Springer, New York, 1984,178-192
- 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)
- 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
- J.
M. Cushing and M. Saleem, A
predator-prey
model with age structure, Journal
of Mathematical Biology 14
(1982), 231-250
- J.
M. Cushing, Periodic
Kolmogorov
systems, SIAM
Journal of
Mathematical Analysis 13, No.
5 (1982), 811-827
- 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
- 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
- J.
M. Cushing and S. D. Simmes, Bifurcation
of asymptotically periodic solutions of Volterra integral
equations, Journal
of Integral
Equations 4 (1980), 339-361
- J.
M. Cushing, Model
stability and
instability in age structured populations, Journal
of Theoretical Biology 86
(1980), 709-730
- J.
M. Cushing, Two
species
competition in a periodic environment, Journal
of Mathematical Biology 10
(1980), 385-400
- 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
- J.
M. Cushing, Nontrivial periodic
solutions of integrodifferential equations, Journal of Integral
Equations 1, No. 2 (1979), 165-181
- 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
- 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
- J.
M. Cushing, Bifurcation
of
periodic oscillations due to delays in single species growth models,
Journal
of Mathematical Biology
6 (1978), 145-161
- J.
M. Cushing, Strongly
admissible
operators and Banach space solutions of nonlinear equations, Funkcialaj
Ekvacioj 20, No. 3
(1977), 237-245
- J.
M. Cushing, On
the
oscillatory
nature
of
general
predator-prey
models with delays, Journal
of
Nonlinear Analysis 1, No. 6
(1977), 583-592
- 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
- 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
- J.
M. Cushing, Time
delays
in single species growth models, Journal
of Mathematical Biology 3
(1977), 257-264
- J.
M. Cushing, Periodic
time-dependent
predator-prey systems, SIAM
Journal of Applied Mathematics
32, No. 1 (1977), 82-95
- J.
M. Cushing, Time delays in
predator-prey systems, Nonlinear
Systems and Applications (V.
Lakshmikantham, ed.), 469-472,
Academic Press, New York, 1977
- J.
M. Cushing, Admissible
operators and solutions of perturbed operator equations, Funkcialaj
Ekvacioj 19 (1976), 79-84
- J.
M. Cushing, Bounded
solutions of perturbed Volterra integro-differential systems, Journal
of Differential Equations
20, No.1 (1976), 61-70
- 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
- J.
M. Cushing, Extremal
tests
for functions of
several real variables at degenerate critical points, Aequationes
Mathematicae 13
(1976), 89-96
- 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
- J.
M. Cushing, Periodic
solutions
of
two
species
interaction
models
with lags, Mathematical
Biosciences 31 (1976), 143-156
- 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)
- J.
M. Cushing, Predator-prey
interactions with time delays, Journal
of Mathematical Biology 3
(1976), 369-380
- J.
M. Cushing, Stable
limit cycles of time dependent multi-species interactions, Mathematical
Biosciences 31 (1976),
259-273
- 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
- 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
- J.
M. Cushing, An
operator
equation and bounded
solutions of integro-differential systems, SIAM
Journal of Mathematical Analysis
6, No. 3 (1975), 433-445
- J.
M. Bownds and J. M. Cushing, Some
stability theorems for systems of Volterra integral equations, Applicable
Analysis 5 (1975), 65-78
- J.
M. Cushing, Stability
of
perturbed Volterra integral equations, Journal
of Mathematical Analysis and
Applications 50, No. 2
(1975), 325-340
- J.
M. Cushing, Nonlinear
Steklov problems on nonsymmetric domains, Journal
of Mathematical Analysis and
Applications 43 (1973),
743-753
- J.
M. Bownds and J. M. Cushing, On
strong stability for linear integral equations, Mathematical
Systems Theory 7, No.
3 (l973), 193-200
- 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
- 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
- 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
- J.
M. Cushing, Nonlinear
Steklov
problems on the unit circle I, Journal
of Mathematical Analysis and Applications
38, No. 3 (1972),
766-783
- 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
- J.
M. Cushing, Some existence results
for Nonlinear Steklov problems, Lecture
Notes in Mathematics, Vol.
280, 236-240, Springer, New York, 1972
- J.
M. Cushing, Global
branches
of
solutions
to
nonlinear
elliptic
eigenvalue problems, Indiana
University Mathematics Journal 20,
No. 11 (1971), 1035-1045
- 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
- 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
- J.
M. Cushing, Uniqueness
of
positive solutions to nonlinear elliptic equations, SIAM
Journal of Mathematical Analysis
2, No. 2 (1971), 290-292
- 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
- J.
M. Cushing, Local
uniqueness for harmonic functions under nonlinear boundary conditions, Journal of Differential
Equations 8,
No. 3 (1970), 512-522
- 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.
- 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