In this paper, the plant–herbivore systems in arid/semi-arid regions are represented by a reaction–diffusion model with delay and nonlocal effects. First, the local asymptotic stability of the non-negative equilibria is proved. Next, the threshold conditions for Turing bifurcation and Hopf bifurcation induced by the time delay are obtained. A linear time-delay state feedback controller is designed to effectively stabilize Turing instability and delay periodic oscillations. Then, the nonlocal spatial interactions not only induce spatially heterogeneous periodic solutions but also drive the system into chaotic states, ultimately leading to ecological collapse. By designing a hybrid parameter-state feedback controller, joint regulation of chaotic phenomena and Turing patterns is achieved successfully, while maintaining equilibrium stability with global diffusion parameters. Furthermore, the combined action of delay and nonlocal competition disrupts spatiotemporal steady states, forming ecological patterns characterized by spatial order and temporal chaos. Moreover, a nonlinear time-delay controller is designed, which simultaneously eliminates chaos, delays periodic oscillations and preserves spatial pattern stability. Finally, numerical simulations validate the theoretical findings. Results confirm that spatiotemporal nonlocal effect profoundly influences plant spatial distribution and dynamic evolution. The developed multimodal control strategies provide a theoretical foundation for ecological management.
Wang et al. (Sat,) studied this question.