DYNAMIC BEHAVIOR OF A NONLINEAR SINGLE SPECIES DIFFUSIVE SYSTEM

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*} where bi(t), aik(t), Dij(t), i, j = 1, 2,…, n; k = 1, 2,…, li are all continuous ω-periodic functions, and βik, i = 1, 2,…, n; k = 1, 2,…, li are 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.