Bifurcation, Pattern Recognition and Numerical Implementations for a Diffusive Predator-Prey System with Weak Allee Effect
This paper is concerned with the dynamical properties of a simplified predator-prey system with weak Allee effect in prey. For the unique positive equilibrium point, we first gives the locally asymptotic stability of ODE system, then study the Turing instability of PDE system. Second, we perform a detailed Hopf bifurcation analysis to both ODE and PDE systems. In particular, we mainly investigate the effects of diffusion coefficient d v and consumption rate b on dynamics in ODE and PDE systems, such as linear stability, periodic solution and limit cycle in temporal system; Turing instability, Turing pattern and Hopf bifurcation in spatiotemporal system