Stability of a periodic solution for a system of parabolic equations

Abstract

In this paper we study the stability of a periodic solution for system of parabolic equations with Neumann boundary conditions. This periodic solution is also solution of an ODE. We compute the Floquet exponents for the linearized system of parabolic equations around this periodic solution. If the diffusion coefficients are close each others and the Floquet exponents for the linearized system of ODE'S around this periodic solution are such that: zero is simple and the others have negative real part, then we prove that this periodic solution is orbitally asymptotically stable for the system of parabolic equations with Neumann boundary conditions.

Keywords:

• system of parabolic equations,
• periodic solution,
• Floquet exponents,
• orbital stability