Stability, co-dimension two bifurcations and chaos control of a host-parasitoid model with mutual interference

In host-parasitiod models, it is widely accepted that mutual interference of parasitoids has stabilizing effect. Conversely, parasitoids interference might significantly destabilize host-parasitoid model dynamics as well. To characterize such dynamics, a host-parasitoid model with mutual interference is investigated. First, we examine the uniformly boundedness of the present model solutions. Then, the existence and uniqueness of the positive fixed point are discussed. Moreover, the parametric conditions of the positive fixed point stability are derived. Besides, we explored the bifurcation behaviors involving 1:2 resonance, 1:3 resonance and 1:4 resonance using normal form approach of discrete-time models and bifurcation theory. In this method, it is not required to switch into Jordan form and compute the center manifold approximation of the present map. It is sufficient to calculate the critical non-degeneracy coefficients to check the listed bifurcation types. Furthermore, the state delayed feedback control technique is applied to regulate the chaotic behaviors of the model. Finally, numerical simulations are provided to support our theoretical results. •A host-parasitoid model with mutual interference is discussed.•Local stability of the positive fixed point is proved.•Co-dimension two bifurcations with 1:2, 1:3, and 1:4 resonance are studied.•Numerical simulations are performed to show the validation of theoretical analysis.•Theoretical study and numerical modeling characterize certain biological phenomena.