BIFURCATION AND CONTROL OF A PREDATOR-PREY SYSTEM WITH TWO TIME DELAYS

To describe the dynamic behavior within ecosystems, we develop a novel predator-prey model that incorporates two distinct time delays in this research. Firstly, by employing fixed-point theorem, inequality technique, and construct an appropriate function, the trait (e.g., existence, uniqueness, non-negativity) of the solution of this delayed predator-prey model is proved. Secondly, the critical value of time delay of this system's stability is sought and the stability and Hopf bifurcation of this model are investigated. A new delay-independent criterion for the stability and bifurcation of this model is presented. Lastly, three delay feedback controllers are designed to adjust the stability region and the onset of bifurcation phenomena of this model. The parameter conditions of this system to maintain stability under the delay feedback controller and the bifurcation phenomenon are discussed. Furthermore, the correctness of the conclusions derived from this study is verified through simulation experiments.