CROSS-DIFFUSION INDUCED INSTABILITY IN LVLEV–TANNER MODEL

Abstract

A Lvlev–Tanner model with cross-diffusion is considered. We analyze the positive uniform steady state and obtain conditions on the parameter values such that the homogeneous steady state is locally asymptotically stable both in the related ODE system and in the PDE system with self-diffusion. Once also cross-diffusion is considered in the model, the uniform steady state is shown to be unstable under some conditions. Numerical simulations are also presented.