Investigating the Nonlinear Behavior of a Predator-Prey Model: A Bifurcation Analysis Approach
摘要
This study delves into the analysis of bifurcation scenarios in a discrete-time predator-prey model featuring a Holling type-II functional response. The model comprises two nonlinear difference equations that portray the interactions between predator and prey populations. By examining the stability of fixed points and the existence of periodic solutions, we unveil diverse bifurcation scenarios, such as period-doubling bifurcation, Neimark-Sacker bifurcation, and strong resonance bifurcations. We further investigate the parameter space where these bifurcations occur and illustrate their impacts on the dynamics of the predator-prey system. Our findings offer valuable insights into the intricate dynamics of predator-prey models and bear significance for the management and conservation of ecological systems.