Time-asymptotic convergence rates towards the discrete evolutionary stable distribution

Author:

Cai Wenli1,Jabin Pierre-Emmanuel2,Liu Hailiang3

Affiliation:

1. Department of Mathematics, China University of Mining and Technology, Beijing 100083, P. R. China

2. Department of Mathematics, University of Maryland, College Park, MD 20742-3289, USA

3. Mathematics Department, Iowa State University, Ames, IA 50011, USA

Abstract

This paper is concerned with the discrete dynamics of an integro-differential model that describes the evolution of a population structured with respect to a continuous trait. Various time-asymptotic convergence rates towards the discrete evolutionary stable distribution (ESD) are established. For some special ESD satisfying a strict sign condition, the exponential convergence rates are obtained for both semi-discrete and fully discrete schemes. Towards the general ESD, the algebraic convergence rate that we find is consistent with the known result for the continuous model.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation

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