Permanence in N species nonautonomous competitive reaction–diffusion–advection system of Kolmogorov type in heterogeneous environment.

摘要

One of the important concept in population dynamics is finding conditions under which the population can coexist. Mathematically formulation of this problem we call permanence or uniform persistence. In this paper we consider N species nonautonomous competitive reaction–diffusion–advection system of Kolmogorov type in heterogeneous environment. Applying Ahmad and Lazer’s definitions of lower and upper averages of a function and using the sub- and supersolution methods for PDEs we give sufficient conditions for permanence in such models. We give also a lower estimation on the numbers δi which appear in the definition of permanence in form of parameters of system ( ?ui ?t = ?[μi?ui ? αiui? ? fi(x)] + fi(t, x, u1, . . . , uN)ui , t > 0, x ∈ ?, i = 1, . . . , N, Diui = 0, t > 0, x ∈ ??, i = 1, . . . , N.