Dynamics and pattern formation of a diffusive predator - prey model in the subdiffusive regime in presence of toxicity

Motivated by the fact that restrictive conditions for a Turing instability are relaxed in subdiffusive regime, we investigate effects of subdiffusion predator - prey model with toxins under homogeneous Neumann boundary condition. First, stability analysis corresponding ordinary differential equation is carried out. From this analysis, it follows closely related to coefficient toxicity. In addition, temporal fractional derivative does not systematically widen range parameters maintain point domain. Furthermore, derive condition which links toxicity regime. System varied order test our mathematical predictions while comparing them ecological literature. It turns out memory effects, linked transport process can, depending on parameters, either stabilize an ecosystem or make completely different configuration.