A two-patch ecological system with nonlinear transfer rate and noise effect

Dynamics of Partial Differential Equations

Volumn 5, Issue 3, 2008, Pages 281-298

  Ma, Suqi ^a   Feng, Zhaosheng ^b   Lu, Qishao ^c  

^a CHINA AGRICULTURAL UNIVERSITY   (China)

^b UNIVERSITY OF TEXAS PAN AMERICAN   (United States)

^c BEIHANG UNIVERSITY   (China)

Author keywords

Center manifold; Delay differential equation; Hopf bifurcation; Noise effect; Poincar normal form; Stochastic equation; Synchronization solution

Indexed keywords

EID: 55349087265     PISSN: 1548159X     EISSN: None     Source Type: Journal    
DOI: 10.4310/dpde.2008.v5.n3.a4     Document Type: Article

References (22)

1. J. D. Murray, Mathematical Biology, Springer-Verlag, New York, 1993.
2. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, Boston, 1993.
3. W. Wischert, A. Wunderlin, A. Pelster, M. Olivier and J. Groslambert, Delay induced instabilities in nonlinear feedback systems, Phys. Rev. E 49 (1994), 203-214.
4. K. Miyakawa and K. Yamada, Entrainment in coupled salt-water oscillators, Phys. D 127 (1999), 177-186.
5. M. E. Starzak, Mathematical Methods in Chemistry and Physics, Springer, New York, 1989.
6. L. Wang and X. Zou, Stability and bifurcation of bidirectional associative memory neural networks with delayed self-feedback, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 15 (2005), 2145-2159.
7. J. D. Murray, Mathematical Biology, Springer-Verlag, New York, 2004.
8. W. G. Aiello and H. I. Freedman, A time-delay model of single-species growth with stage structure, Math. Biosci. 101 (1990), 139-153.
9. W. G. Aiello, H. I. Freedman and J. Wu, Analysis of a model representing stage-structured population growth with state-dependent time delay, SIAM J. Appl. Math. 52 (1992), 855-869.
10. Y. Kuang and J. W. H. So, Analysis of a delayed two-stage population model with space-limited recruitment, SIAM J. Appl. Math. 55 (1995), 1675-1696.
11. E. Beretta and Y. Kuang, Geometrical stability switch criteria delay differential systems with delay dependent parameters, SIAM J. Math. Anal. 33 (2002), 1144-1165.
12. S. A. Gourley and Y. Kuang, A stage structured predator-prey model and its dependence on maturation delay and death rate, J. Math. Biol. 49 (2004), 188-200.
13. K. L. Cooke and P. van den Driessche, On zeros of some transcendental equations, Funkcial EKvac. 29 (1986), 77-90.
14. K. L. Cooke, P. van den Driessche and X. Zou, Interaction of maturation delay and nonlinear birth in population and epidemic models, J. Math. Biol. 39 (1999), 332-352.
15. S. Q. Ma, Q. S. Lu and S. L. Mei, Dynamics of a logistic population model with maturation delay and nonlinear birth rate, Discrete Contin. Dyn. Syst. Ser. B 5 (2005), 735-752.
16. J. Z. Lei and M. C. Mackey, Stochastic differential delay equation, moment stability, and application to hemropoietic stem cell regulation system, SIAM J. Appl. Math. 67 (2007), 387-407.
17. Y. Qu and J. J. Wei, Bifurcation analysis in a time-delay model for prey-predator growth with stage-structure, Nonlin. Dyn. 49 (2007), 285-294.
18. S. Petrovskii, H. Malchow and B. L. li, An exact solution of a diffusive predator-prey system, Proc. R. Soc. A 461 (2005), 1029-1053.
19. S. B. Hsu, T. W. Hwang and Y. Kuang, Global analysis of the MichaelisMenten ratio-dependent predator-prey system, J. Math. Biol. 42 (2001), 489-506.
20. A. Longtin, Effects of noise on nonlinear dynamics, in Nonlinear Dynamics in Physiology and Medicine (A. Beuter, L. Glass, M. C. Mackey, and M. S. Titcombe, eds.), pp. 149-189, Springer-Verlag, New York, 2003.
21. K. Burrage, P. M. Burrage and T. Tian, Numerical methods for strong solutions of stochastic differential equations: An overview, Proc. R. Soc. Lond. A 460 (2004), 373-402.
22. B. Øksendal, Stochastic Differential Equations: An Introduction with Applications, 6th ed., Springer-Verlag, New York, 2003.