DYNAMIC BEHAVIOR OF A NONLINEAR SINGLE SPECIES DIFFUSIVE SYSTEM

Fengde Chen (), Xiaoxing Chen and Jinlin Shi
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Fengde Chen: College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350002, China
Xiaoxing Chen: College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350002, China
Jinlin Shi: College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350002, China

Advances in Complex Systems (ACS), 2005, vol. 08, issue 04, 399-417

Abstract: In this paper, we consider the following nonlinear single species diffusive system\begin{eqnarray*} \dot{x}_i(t)&=& x_i(t)\left(b_i(t)-\sum_{k=1}^{l_i}a_{ik}(t)(x_i(t))^{\beta_{ik}}\right)\\ && +\,\sum_{j=1}^{n}D_{ij}(t)(x_j(t)-x_i(t)),\quad (i,j=1,2,\ldots,n), \end{eqnarray*}wherebi(t),aik(t),Dij(t),i, j = 1, 2,…, n;k = 1, 2,…, liare all continuous ω-periodic functions, andβik,i = 1, 2,…, n;k = 1, 2,…, liare positive constants. Sufficient conditions which guarantee the permanence, extinction and existence of a unique globally attractive positive ω-periodic solution are obtained. Examples together with their numeric simulations show the feasibility of the main results.

Keywords: Periodic solution; permanence; nonlinear single species; diffusion; stability (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1142/S021952590500049X

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