Stability and Bifurcation of a Time‐Varying Delay Generalist Food Chain Model With Double Fear Effect

ABSTRACT In this paper, we mainly consider a three‐species predator‐prey model incorporating fear effect, additional food, time‐varying delay, and cannibalistic intermediate predator. First, for the model without time delay, not only the positivity and boundedness of solutions are investigated, but also some conditions for local asymptotic stability of all possible equilibriums and global stability of the positive equilibrium are obtained. Then, some conditions for the existence of a Hopf bifurcation of the model with time delay are explored. Next, the global stability of the positive equilibrium of such a model with time‐varying delay is investigated. Furthermore, the multiple time scales method is applied to the delay differential system, and a control strategy based on time delay is obtained. Specifically, a time‐varying perturbation is introduced to the delay to suppress oscillation. Finally, the theoretical findings are validated through numerical simulations.