Codimension two bifurcation and spatiotemporal patterns in a diffusive predator-prey system

时   间：  2023-04-10 14:30 — 16:00

In this talk, taking a diffusive predator-prey system with no-flux boundary conditions as an example, we define and describe the first bifurcation curve, which shows that the coexistence equilibrium can lose its stability through not only codimension one Turing (Hopf) bifurcation, but also codimension two Turing-Hopf, Turing-Turing, Double Hopf and Bogdanov-Takens bifurcations, etc. In addition, the explicit formulas for the coefficients of normal forms for Turing-Hopf，Double Hopf and Bogdanov-Takens bifurcations of general PFDEs involving nonlocal interactions, are presented concisely. Some new spatiotemporal patterns are theoretically predicted and shown numerically.