Bifurcation and Stability Analysis of a New Fractional-Order Prey–Predator Model with Fear Effects in Toxic Injections

Abstract

This paper proposes a prey–predator model affected by fear effects and toxic substances. We used the Lipschitz condition to prove the uniqueness of the model solution and Laplace transform to prove the boundedness of the model solution. We used the fractional-order stability theorem to provide sufficient conditions for the local stability of equilibrium points, and selected fractional-order derivatives as parameters to perform Hopf bifurcation analysis on the system. Finally, the theoretical results are verified via numerical simulation. The results show that a value of α will affect the stability of the system and that the population size and the effect of toxic substances have a huge impact on the stability of the system.

Keywords

• prey–predator model
• fractional-order system
• fear effect
• toxic injections
• Holling II functional response