E. M. Elsayed and Qamar Din
Larch Budmoth Interaction: Stability, Bifurcation and Chaos Control
Dynamic Systems and Applications 32 (2023) 199-229

https://doi.org/10.46719/dsa2023.32.12

ABSTRACT.
Taking into account the interaction between budmoth and 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 Holling type III functional response for interaction of plant quality. The proposed functional response is validated with real observed data of larch budmoth interaction. Furthermore, we investigate qualitative behavior of this proposed discrete-time system for interaction between budmoth and quality of larch trees. Boundedness of solutions, existence of fixed points and their local behavior is carried out. It is proved that system experiences period-doubling bifurcation at its positive fixed point with utilizing center manifold theorem and normal forms theory. Moreover, existence and direction for Neimark-Sacker bifurcation are also investigated for larch budmoth interaction. Bifurcating and fluctuating behaviors of system are controlled through utilization of chaos control strategies. Numerical simulations are presented to demonstrate the theoretical findings. At the end, theoretical investigations are validated with
field and experimental data.

AMS (MOS) Subject Classification. 39A30, 40A05, 92D25,92C50.

Key Words and Phrases. Larch budmoth interaction; stability; period-doubling bifurcation;
Neimark-Sacker bifurcation; chaos control.