DIFFUSION-DRIVEN INSTABILITY AND WAVE PATTERNS OF LESLIE–GOWER COMPETITION MODEL

Abstract

In this paper, the diffusion-driven instability of the Leslie–Gower competition model with the periodic boundary conditions is investigated. By using the linearization method and the inner product techniques, the instability conditions of this model at the coexistence fixed point and the competitive exclusion fixed points are obtained, respectively. As an example, the diffusion-driven instability conditions of a symmetric Leslie–Gower competition model at the coexistence fixed point is obtained when the diffusion coefficients are equal. Under these instability conditions, various patterns, including spirals, traveling waves and disorders, are observed in the numerical simulations. On the other hand, we also numerically investigate the effects of diffusion coefficient and the strength of the interspecific competition on the wave patterns.