Travelling wave patterns and bifurcation dynamics in a spatial predator–prey model

We have studied a diffusive predator–prey model with nonlinear predator–prey interactions and prey dispersal. Using bifurcation analysis combined with numerical simulations, we reveal a rich variety of dynamical behaviors, including the stability of steady states, wave fronts, wave pulses, periodic and multi-periodic wave trains, and chaotic spatiotemporal patterns. The results show that diffusion and interaction strength play a critical role in shaping the travelling-wave dynamics through saddle–node, Hopf, and period–doubling bifurcations. In particular, increasing diffusion can destabilize steady states and induce oscillatory dynamics, ultimately leading to chaotic population fluctuations. These findings provide ecological insight into how spatial dispersal and nonlinear interactions shape complex population patterns in predator–prey systems.

کلیدواژه ها:

Predator-Prey model ، Travelling waves ، Stability analysis ، Bifurcation