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February  2003, 3(1): 69-78. doi: 10.3934/dcdsb.2003.3.69

Global periodicity in a class of reaction-diffusion systems with time delays

Wei Feng 1, and  Xin Lu 2,

1. 

Department of Mathematics and Statistics, University of North Carolina in Wilmington, Wilmington, NC 28403, United States
2. 

Department of Math and Stat. UNCW, 601 S. College Road, Wilmington NC 28403, United States

Received  November 2001 Revised  October 2002 Published  November 2002

In this paper we study a class of reaction-diffusion systems modelling the dynamics of "food-limited" populations with periodic environmental data and time delays. The existence of a global attracting positive periodic solution is first established in the model without time delay. It is further shown that as long as the magnitude of the instantaneous self-limitation effects is larger than that of the time-delay effects, the positive periodic solution is also the global attractor in the time-delay system. Numerical simulations for both cases (with or without time delays) demonstrate the same asymptotic behavior (extinction or converging to the positive $T$-periodic solution, depending on the growth rate of the species).
Keywords: Reaction-diffusion systems, time-delay system..
Mathematics Subject Classification: Primary: 34A34, 34D23, 92D25; Secondary: 65L0.
Citation: Wei Feng, Xin Lu. Global periodicity in a class of reaction-diffusion systems with time delays. Discrete & Continuous Dynamical Systems - B, 2003, 3 (1) : 69-78. doi: 10.3934/dcdsb.2003.3.69
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