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Dynamic Behavior Of A Nonlinear Single Species Diffusive System

Author

Listed:
  • 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)

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.

Suggested Citation

  • Fengde Chen & Xiaoxing Chen & Jinlin Shi, 2005. "Dynamic Behavior Of A Nonlinear Single Species Diffusive System," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 8(04), pages 399-417.
    • Handle: RePEc:wsi:acsxxx:v:08:y:2005:i:04:n:s021952590500049x
    DOI: 10.1142/S021952590500049X
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