Stability and Bifurcation Analysis of a Phytoplankton-Zooplankton Model with Linear Functional Responses

Abstract

In this paper, the dynamics of a phytoplankton-zooplankton system with linear functional responses are examined. For the continuous-time model, the global asymptotic stability of the fixed points is demonstrated by constructing Lyapunov functions. For the discrete version of the model, both local and global dynamics are investigated using LaSalle's Invariance Principle. Furthermore, the occurrence of a Neimark-Sacker bifurcation at the positive fixed point is established, and it is proved that the resulting invariant closed curve is attracting.