Stability, bifurcation and high-dimensional Turing pattern of a diffusive pine wilt disease system

This paper reports the complex dynamical phenomena of a diffusive pine wilt disease model. In the absence of diffusion, we examine the existence, stability, and types of various equilibria of the system. For the diffusive pine wilt disease system, we first establish the boundedness of classical solutions. Additionally, the stability of the equilibria for the reaction–diffusion system is derived. We also establish the conditions for the existence of Turing instability and Turing–Hopf bifurcation. Finally, the numerical simulation results fully validate the reliability of the theoretical conclusions. A variety of complex pattern formations are presented in different dimensional spaces, such as stripe patterns, spot patterns, and target patterns, among others. These numerical results indicate that the selection of spatiotemporal pattern modes in the system varies depending on the vicinity of different bifurcations and under different initial perturbation conditions. We believe that the theoretical and numerical results provide valuable insights into exploring the bifurcation dynamics and the complex patterns in this pine wilt disease system.