Analysis of Dynamic Properties of Forest Beetle Outbreak Model (Journal of Nonlinear Modeling and Analysis, 2024)
This paper mainly studies the dynamic properties of the forestbeetle outbreak model. The existence of the positive equilibrium point andthe local stability of the positive equilibrium point of the system are analyzed,and the relevant conclusions are drawn. After that, the existence of Turinginstability, Hopf bifurcation and Turing-Hopf bifurcation are discussed respectively, and the necessary conditions for existence are given. Finally, the normalform of the Turing-Hopf point is calculated, and some dynamic properties atthe point are analyzed by numerical simulation.
Keywords: Reaction-diffusion equation; Turing instability; Hopf bifurcation; Turing-Hopf bifurcation.