Dynamics of a delayed reaction-diffusion predator-prey model with the effect of the toxins

Abstract

In this study, we investigate a delayed reaction-diffusion predator-prey system with the effect of toxins. We first investigate whether the internal equilibrium exists. We then provide certain requirements for the presence of Turing and Hopf bifurcations by examining the corresponding characteristic equation. We also study Turing-Hopf and Hopf bifurcations brought on by delays. Finally, numerical simulations that exemplify our theoretical findings are provided. The quantitatively obtained properties are in good agreement with the findings that the theory had predicted. The effects of toxins on the system are substantial, according to theoretical and numerical calculations.

Keywords

• toxins
• delay
• diffusion
• bifurcation
• spatial pattern