The effect of periodic habitat fluctuations on a nonlinear insect population model

Journal of Mathematical Biology

Volumn 36, Issue 2, 1997, Pages 201-226

  Henson, Shandelle M ^a   Cushing, J M ^a  

^a University of Arizona   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001737892     PISSN: 03036812     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002850050098     Document Type: Article

References (55)

1. Abrams, P., 1984. Variability in resource consumption rates and the coexistence of competing species, Theor. Pop. Biol. 25: 106-124
2. Bardi, M. and A. Schiaffino, 1982. Asymptotic behaviour of positive solutions of periodic delay logistic equations, J. Math. Biol. 14: 95-100
3. Bardi, M., 1983. An Equation of growth of a single species with realistic dependence on crowding and seasonal factors, J. Math. Biol. 17: 33-43
4. Boyce, M. S. and D. J. Daley, 1980. Population tracking of fluctuating environments and natural selection for tracking ability, Amer. Nat. 115: 480-491
5. Chesson, P. L., 1982. The stabilizing effect of a random environment, J. Math. Biol. 15: 1-36
6. Chesson, P. L., 1986. Environmental variation and the coexistence of species. Community Ecology, J. Diamond and T. J. Case (Eds.), Harper and Row, New York, pp. 240-256
7. Chesson, P. L., 1991. Stochastic population models, appearing in Ecological Heterogeneity, J. Kolasa and S. Pickett (eds.), Springer, New York, pp. 123-143
8. Chesson, P. L. and T. J. Case, 1986. Nonequilibrium community theories: chance, variability, history, and coexistence, Community Ecology, J. Diamond and T. J. Case (Eds.), Harper and Row, New York, pp. 229-239
9. Chesson, P. L. and S. Ellner, 1989. Invasibility and stochastic boundedness in monotonic competition models, J. Math. Biol. 27: 117-138
10. Chesson, P. L. and R. R. Warner, 1981. Environmental variability promotes coexistence in lottery competitive systems, Am. Nat. 117: 923-943
11. Cohen, D. S. and S. Rosenblat, 1982. A delay logistic equation with variable growth rate, SIAM J. Appl. Math. 42: 608-624
12. Coleman, B. D., 1979. Nonautonomous logistic equations as models of the adjustment of populations to environmental change, Math. Biosci. 45: 159-173
13. Costantino, R. F. and R. A. Desharnais, 1991. Population Dynamics and the Tribolium Model: Genetics and Demography, Monographs on Theoretical and Applied Genetics 13, Springer, Berlin
14. Costantino, R. F., J. M. Cushing, B. Dennis and R. A. Desharnais, 1995. Experimentally induced transitions in the dynamic behaviour of insect populations, Nature 375: 227-230
15. Costantino, R. F., R. A. Desharnais, J. M. Cushing and B. Dennis, 1997. Chaotic dynamics in an insect population, Science 275: 389-391
16. Costantino, R. F., J. M., Cushing, B. Dennis, R. A. Desharnais, S. M. Henson, 1997. Resonant population cycles in alternating habitats, to appear in Bull. Math. Biol.
17. Cushing, J. M., 1977. Periodic time-dependent predator-prey systems, SIAM J. Appl. Math. 32: 82-95
18. Cushing, J. M., 1980. Two species competition in a periodic environment, J. Math. Biol. 10: 385-400
19. Cushing, J. M., 1982. Periodic Kolmogorov systems, SIAM J. Math. Anal. 13: 811-827
20. Cushing, J. M., 1983. Periodic Lotka-Volterra systems and time sharing of ecological niches, Lecture Notes in Biomathematics 52, Springer, Berlin, pp. 342-348
21. Cushing, J. M., 1984. Periodic two-predator, one-prey interactions and the time sharing of a resource niche, SIAM J. Appl. Math. 44: 392-410
22. Cushing, J. M., 1987. Oscillatory population growth in periodic environments, Theor. Pop. Biol. 30: 289-308
23. Cushing, J. M., 1995. 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 (Eds), Gordon and Breach Publishers, US, 1995, pp. 123-132
24. Cushing, J. M. and Zhou Yicang, 1994. The net reproductive value and stability in matrix population models, Nat. Res. Model, 8(4) : 297-333
25. Cushing, J. M., B. Dennis, R. A. Desharnais and R. F. Costantino, 1996. An interdisciplinary approach to understanding nonlinear ecological dynamics, Ecological Modelling 92: 111-119
26. de Mottini, P. and A. Schiaffino, 1979. On logistic equations with time periodic coefficients, I.A.C. Mauro Picone, Series III, No. 192, Rome
27. de Mottini, P. and A. Schiaffino, 1981. Competition systems with periodic coefficients: A geometric approach, J. Math. Biol. 11: 319-335
28. Dennis, B., R. A. Desharnais, J. M. Cushing and R. F. Costantino, 1995. Nonlinear demographic dynamics: Mathematical models, statistical methods, and biological experiments, Ecol. Monogr. 65(3): 261-281
29. Dennis, B., R. A. Desharnais, J. M. Cushing and R. F. Costantino, 1997. Transitions in population dynamics: equilibria to periodic cycles to aperiodic cycles, to appear in J. Animal Ecology
30. Ellner, S., 1987. Alternate plant life history strategies and coexistence in randomly varying environments, Vegetatio 69: 199-208
31. Ellner, S., 1989. Convergence to stationary distributions in two species competition models, J. Math. Biol. 27: 451-462
32. Gantmacher, F. R., 1959. The Theory of Matrices, Vol. II. Chelsea Publishing Company, New York
33. Guckenheimer, J. and P. Holmes, 1983. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York, p. 18
34. Hale, J. K., 1988. Asymptotic behavior of dissipative systems, Math. Surveys Monogr. 25, Amer. Math. Soc., Providence. pp. 13,19
35. Hale, J. K. and A. S. Somolinos, 1983. Competition for fluctuating nutrient, J. Math. Biol. 18: 255-280
36. Hsu, S. B., 1980. A competition model for a seasonally fluctuating nutrient, J. Math. Biol. 9: 115-132
37. Henson, S. M., 1996. Existence and stability of nontrivial periodic solutions of periodically forced discrete dynamical systems, J. Difference Eqn. and Appl. 2: 1137-1142
38. Henson, S. M., 1996. The effect of periodicity in maps, submitted
39. Hofbauer, J. and J. W. -H. So, 1989. Uniform Persistence and repellors for maps, Proc. Amer. Math. Soc. 107(4): 1137-1142
40. Jillson, D., 1980. Insect populations respond to fluctuating environments, Nature 288: 699-700
41. Kuang, Y. and J. M. Cushing, 1995. Global stability in a nonlinear difference-delay equation model of flour beetle population growth, J. Difference Eqn. and Appl. 2: 31-37
42. Loreau, M., 1989. Coexistence of temporally segregated competitors in a cyclic environment, Theor. Pop. Biol. 36: 181-201
43. May, R. M., 1973. Stability and complexity in model ecosystems, Princeton University Press, p. 123
44. May, R. M. (Ed.) 1976. Theoretical Ecology. W. B. Saunders, p. 23
45. Murray, J. D., 1989. Mathematical Biology, Vol. 19, Biomathematics, Springer-Verlag, Berlin, p. 702
46. Namba, T., 1984. Competitive co-existence in a seasonally fluctuating environment, J. Theor. Biol. 111: 369-386
47. Namba, T., 1986. Bifurcation phenomena appearing in the Lotka-Volterra competition equations: a numerical study, Math. Biosci. 81: 191-212
48. Nisbet, R. M. and W. S. C. Gurney, 1976. Population dynamics in a periodically varying environment, J. Theor. Biol. 56: 459-475
49. Rosenblat, S., 1980. Population models in a periodically fluctuating environment, J. Math. Biol. 9: 23-36
50. Sanchez, D. A., 1982. Periodic environments, harvesting, and a Riccati equation, Nonlinear Phenomena in Mathematical Sciences, V. Laksmikantham (Ed.), Academic Press, New York
51. Smith, H. L., 1981. Competitive coexistence in an oscillating chemostat, SIAM J. Appl. Math. 40: 498-522
52. Smith, H. L. and P. Waltman, The Theory of the Chemostat, Cambridge Studies in Mathematical Biology, Cambridge University Press, Cambridge, Chapter 7
53. Sonneveld, P. and J. van Dan, 1979. On a conjecture about the periodic solutions of the logistic equations, J. Math. Biol. 8: 285-289
54. Stanley, J., 1932. A mathematical theory of the growth of populations of the flour beetle, Tribolium confusum, Duv. Can. J. Res. 6: 632-671
55. Turelli, M., 1981. Niche overlap and invasion of competitors in random environments I. Models without demographic stochasticity, Theor. Pop. Biol. 20: 1-56