Dynamics analysis of a stage-structure predator-prey model of Bactericera gobica Loginova

The Bactericera gobica Loginova is a key pest in Lycium barbarum L. cultivation, and understanding its population dynamics and their trophic interactions with natural enemies is crucial for developing effective pest management strategies. This study develops a stage-structure predator-prey model of Bactericera gobica Loginova populations based on their biological characteristics, with the population divided into nymph and adult developmental stages under the fundamental assumption of exclusive nymphal predation by natural enemies. Theoretical analysis establishes the existence, uniqueness and boundedness of the solution. Stability analysis examines the local asymptotic stability of equilibria, while Lyapunov function theory and LaSalle’s invariance principle are applied to investigate global asymptotic stability. The system is shown to exhibit transcritical bifurcation through Sotomayor’s theorem, with Hopf bifurcation theory analyzing the emergence conditions and stability characteristics of periodic solutions. Numerical simulations confirm the theoretical results, demonstrating that parameter variations can induce both transcritical and Hopf bifurcations leading to stable limit cycles. Two-parameter bifurcation analysis further identifies distinct parameter regions for stable equilibrium states and periodic oscillations. The results indicate that nymph-adult conversion rates and predation intensity jointly drive system instability and periodic oscillations, providing theoretical guidance for developing biological control strategies based on natural enemies.