Bifurcation and controller design in a 3D delayed predator-prey model

Delayed dynamical models demonstrate significant application value in depicting interactions and internal dynamics among different biological populations. Therefore, they have garnered significant interest from numerous scholars in both biology and mathematics. Based on previous studies, this article construct a novel delayed predator-prey model. By utilizing fixed point theory, inequality methods, and appropriate functions, this article examined the desirable properties of the solutions of the constructed delayed predator-prey system, including existence and uniqueness, boundedness, and non-negativity. This paper determines the parameter conditions for system stability and the occurrence of bifurcations by employing bifurcation theory and the stability theory of delayed differential equations. Using two control strategies, namely the mixed controller and the extended delay feedback controller, this paper effectively adjusts the stability domain of the delayed predator-prey systems and controls the time of bifurcation onset. The research explores how delays affect the stabilization of system and the adjustment of bifurcation. This paper provides computer simulation photos supporting the main obtained findings. The outcomes of this paper are groundbreaking and can provide critical guidance for the control and regulation of predator and prey population densities.