Stability in a diffusive food-chain model with Michaelis-Menten functional response
This paper concerns the asymptotic behaviour of the solutions to a system of nonlinear parabolic equations with homogeneous Neumann boundary conditions and initial conditions. The investigated system describes the predator-prey biological model for three species in which the third one is the predator of the second one and the second one is the predator of the first one. The system is of a reaction-diffusion type. A sufficient condition for local asymptotic stability is given by linearization and for global asymptotic stability is given by a Lyapunov function.
scientific article; zbMATH DE number 2102514
scientific article