# American Institute of Mathematical Sciences

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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

 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).
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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