Affiliation: | 1. College of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, PR China;2. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, PR China |
Abstract: | This paper aims at providing an alternative approach to study global dynamic properties for a two-species chemotaxis model, with the main novelty being that both populations mutually compete with the other on account of the Lotka–Volterra dynamics. More precisely, we consider the following Neumann initial–boundary value problem in a bounded domain , with smooth boundary, where are positive constants.When and , it is shown that under some explicit largeness assumptions on the logistic growth coefficients and , the corresponding Neumann initial–boundary value problem possesses a unique global bounded solution which moreover approaches a unique positive homogeneous steady state of above system in the large time limit. The respective decay rate of this convergence is shown to be exponential.When and , if is suitable large, for all sufficiently regular nonnegative initial data and with and , the globally bounded solution of above system will stabilize toward as in algebraic. |