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

Wei Feng; Xin Lu

doi:10.3934/dcdsb.2003.3.69

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2003, Volume 3, Issue 1: 69-78. Doi: 10.3934/dcdsb.2003.3.69

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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
2.
Department of Math and Stat. UNCW, 601 S. College Road, Wilmington NC 28403

Received: October 31, 2001

Revised: September 30, 2002

Published: January 2003

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Abstract

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: 65L07.

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