Bifurcation Analysis of a Discrete Predator-Prey Model with Fear Effects, Prey Refuge, Harvesting and Crowley-Martin Functions

In this article, we consider a discrete predator-prey model with fear effects, prey refuge, harvesting and Crowley-Martin functional responses. First, we analyze the existence of the model's fixed points. Subsequently, we apply bifurcation theory to establish the conditions for the occurrence of fold-flip bifurcation, 1:1 strong resonance and 1:2 strong resonance. Finally, we verify our theoretical analysis through numerical simulations, presenting bifurcation diagrams, maximum Lyapunov exponents diagrams, phase portraits, and the two-parameter spaces under the specified initial conditions.