TITLE:
Bifurcation Analysis of a Hyphantria cunea-Chouioia cunea Yang Model with Nonlocal Competition for Biological Control
AUTHORS:
Xiaoxue Xia, Yujuan Gao, Yuting Ding
KEYWORDS:
H. cunea-C. Cunea Model, Nonlocal Competition, Hopf Bifurcation, Turing Bifurcation, Time Delay, Biological Control
JOURNAL NAME:
International Journal of Modern Nonlinear Theory and Application,
Vol.14 No.2,
June
11,
2025
ABSTRACT: Hyphantria cunea (H. cunea for short) causes serious forest pests and diseases, whereas its parasitic natural enemy, Chouioia cunea Yang (C. cunea for short) can effectively control the amount of H. cunea. Considering the eclosion time of pupae, nonlocal competition and biological control, we establish a biological control model with time delay and nonlocal competition. In this paper, we analyze the conditions for the existence of the Hopf bifurcation and the Turing bifurcation, then derive the normal form of Hopf bifurcation by using multiple time scales method. Finally, a group of real data is used for simulations. Comparing the models with and without nonlocal competition, we conclude that nonlocal competition can induce stable spatially inhomogeneous periodic solutions through Hopf bifurcation, while the model without nonlocal competition can induce spatially homogeneous periodic solutions through Hopf bifurcation. Comparing the models with and without biological control, we find that releasing limited amounts of C. cunea can quickly and effectively control the growth of H. cunea population. We also give the corresponding biological explanations and suggestions.