Stability and fold bifurcation in a three-species model with mutual interference on parasitoids and hyperparasitoids

This study establishes a novel three-species host–parasitoid–hyperparasitoid system with mutual interference effects on parasitoids and hyperparasitoids. We derive the asymptotic stability conditions for the equilibrium points and classify the impacts of hyperparasitoids on the dynamical behavior by comparing these stability conditions. Additionally, we demonstrate the presence of a fold bifurcation in the proposed three-dimensional model using a novel center manifold projection method. Finally, we verify our findings through numerical simulations.