Stability and dynamical bifurcation of a generalized Fisher equation

Abstract:

This research studies the dynamic bifurcation and stability of solutions for a generalized Fisher equation. The complete criterion, types and properties of dynamical bifurcation are obtained by center manifold reduction method and attractor bifurcation theory. Some characterizations of basins of attractors are given. These results improve the known results.Numerical simulations are provided to verify the theoretical analysis.