A note on Turing–Hopf bifurcation in a diffusive Leslie–Gower model with weak Allee effect on prey and fear effect on predator

Abstract

In this paper, we investigate the dynamics of a diffusive Leslie–Gower model incorporating a weak Allee effect on prey and a fear effect on predators. First, we derive the relevant characteristic equations. Subsequently, we analyze the existence of Turing Hopf bifurcation–phenomena that characterize the emergence of spatial patterns and temporal oscillations driven by diffusion and population dynamics, respectively. Finally, we perform numerical simulations to validate our theoretical results and further illustrate the model dynamics with both weak Allee and predator fear effects.