A Plankton Allelopathic Model Described by a Delayed Quasilinear Parabolic System

Abstract

The quasilinear parabolic system has been applied to a variety of physical and engineering problems. However, most works lack effective techniques to deal with the asymptotic stability. This paper is concerned with the existence and stability of solutions for a plankton allelopathic model described by a quasilinear parabolic system, in which the diffusions are density-dependent. By the coupled upper and lower solutions and its associated monotone iterations, it is shown that under some parameter conditions the positive uniform equilibrium is asymptotically stable. Some biological interpretations for our results are given.

Keywords:

• parabolic reaction–diffusion equation
• Volterra equation
• quasi-linearization
• global stability
• existence

AMS Subject Classification:

• 35B35
• 92D50