Nonlinear Dynamics of a Toxin-Phytoplankton-Zooplankton System with Self- and Cross-Diffusion

Figure 1

Bifurcation diagram with and , where the parameters values are taken as , , , , , , , , , , and . The gray line represents , the blue curve represents , and the red curve represents ; thus shows the zone where the instability induced by diffusion occurs. The remainder of this paper is organized as follows. In Section 2, we describe and analyze the toxin-phytoplankton-zooplankton system, and we derive the criteria for the stability and instability of a system with cross-diffusion. In Section 3, we present the results of numerical simulations and discuss their implications. Finally, we give our conclusions in Section 4.