Transient Dynamics of a Food Chain Model with Vigilance in the Biparameter Spaces

This article focuses on the asymptotic and transient behavior of a food chain model with vigilance in the biparameter spaces. Firstly, the local asymptotic stability conditions of the positive equilibrium point are obtained. Then, the transient dynamical behavior of the positive equilibrium point is analyzed based on eight parameters. Using numerical simulation, the stable regions of the model with single and double parameters are plotted, as well as the value changes of resilience, reactivity, and amplification envelope within the stable regions. The results show that the coexistence equilibrium point is always reactive, and the corresponding parameter ranges for system stability are large, but the resilience values are small. The vigilance parameter of the middle- and lower-level organisms has the greatest impact on the system’s resilience and reactivity, and the lowest vigilance corresponds to the maximum resilience and reactivity. Our results provide important references for effective management and protection of wild animal populations by the potential for transient amplification, disturbance growth time, and amplitude.