Stability and Hopf bifurcation analysis of fractional double-delay prey-predator model under PD control strategies

摘要: A fractional-order proportional-derivative controller is designed to address bifurcation issues in a dual-time-delay fractional-order predator-prey model. By selecting different delays as bifurcation parameters, the stability and Hopf bifurcation conditions of the controlled system are derived. The results show that the fractional order, delays and control parameters play an important role on the stability and Hopf bifurcation of the system. By selecting reasonable system parameters (fractional order, delays, and control parameters), suitable system control strategies can be devised. Finally, the key findings of this study are verified through numerical examples.