Global stability and bifurcation analysis of an infochemical induced three species discrete-time phytoplankton–zooplankton model

Abstract

This article analyzes a discrete-time three-species model of phytoplankton and zooplankton with infochemical producing, non-infochemical producing, and zooplankton. It is assumed that the grazing of infochemical producing phytoplankton indirectly increases the mortality rate of zooplankton. The fixed points of the system and their respective local stability has been examined. The conditions for Neimark–Sacker bifurcation along with period doubling bifurcation at the positive fixed point are outlined. The sufficient conditions for global asymptotic stability of the positive fixed point are obtained. The application of a hybrid control strategy effectively stabilizes the chaotic behavior of the system. Lastly, our theoretical discussion is solidified through a numerical simulation which enables us to witness the complex behavior of the system.