Dynamic analysis of the ecosystem of plateau pikas under pulse control

Currently, plateau pikas have become one of the key factors contributing to grassland desertification on the Qinghai–Tibet Plateau. The Chinese government allocates significant funds annually to eradication campaigns. However, recent studies indicate that eliminating plateau pikas is detrimental to the sustainable development of the ecosystem. Therefore, we propose a ratio-dependent pulse control model. Using techniques such as Poincaré mapping and bifurcation theory, we establish the global stability of equilibrium points in the model. By applying fixed-point theorem and vector field analysis, we identify critical conditions for the orbitally asymptotic stability of order-1 and order-2 periodic solutions. Additionally, we provide criteria for the existence and stability of a predator-free periodic solution and conduct bifurcation and sensitivity analyses of relevant parameters. Finally, through numerical simulations, we validate the theorem and confirm the feasibility of the control approach. Theoretical and numerical results indicate that the population of plateau pikas can be maintained at lower levels. This offers a new control strategy for plateau pika management.