Temporal Forcing Induced Pattern Transitions Near the Turing–Hopf Bifurcation in a Plankton System

Abstract

We explore the impact of time-periodic forcing on pattern transitions in a plankton system of reaction–diffusion type. Here, we mainly focus on the forced states near the Turing–Hopf bifurcation. A normal form analysis leads to the finding that weak forcing exhibits a destabilizing effect on the dynamics by exciting the transitions from a spatially homogeneous stationary state to a periodic oscillation in time. The results are obtained by studying the amplitude equations derived using weakly nonlinear analysis in the presence of forcing, which enables us to calculate the changes of states. Examples are given to confirm the theoretical results.