Resumen de A Discrete‑Time Model for Consumer–Resource Interaction with Stability, Bifurcation and Chaos Control
Qamar Din, Muhammad Irfan Khan
Keeping in mind the interactions between budmoths and the quality of larch trees located in the Swiss Alps (a mountain range in Switzerland), a discrete-time model is proposed and studied. The novel model is proposed with implementation of a nonlinear functional response that incorporates plant quality. The proposed functional response is validated with real observed data of larch budmoth interactions.
Furthermore, we investigate the qualitative behavior of the proposed discrete-time system with interactions between budmoths and the quality of larch trees. Proofs of the boundedness of solutions, and the existence of fxed points and their topological classifcation are carried out. It is proved that the system experiences perioddoubling bifurcation at its positive fxed point using the center manifold theorem and normal forms theory. Moreover, existence and direction for the torus bifurcation are also investigated for larch budmoth interactions. Bifurcating and fuctuating behaviors of the system are controlled through utilization of chaos control strategies.
Numerical simulations are presented to demonstrate the theoretical fndings. At the end, theoretical investigations are validated with feld and experimental data.
