Bifurcation Analysis on a Diffusive Minimal Model of Plankton Systems with Stage Structure

Abstract

In this study, we investigate the dynamics of a diffusive minimal plankton model with stage structure. We first establish sufficient conditions for the existence of a unique positive constant steady state. Building on this, we analyze the stability of the equilibrium and examine potential Hopf bifurcations and Turing bifurcations. Based on these results, a bifurcation set is constructed, providing clear insight into how variations in system parameters affect the dynamics. To corroborate the theoretical findings, numerical simulations are conducted, which demonstrate that not only diffusion and maturation delay, but also the predation rate and half-saturation constant, play significant roles in shaping the system behavior. Finally, the main results are summarized and discussed.