Dynamics of a Patch-forming Plankton Model with Toxin Liberation Delay

Abstract We perform a local qualitative analysis of our proposed plankton model to understand recurring harmful algal blooms (HAB) caused by patch-forming toxin-producing phytoplankton (TPP) interacting with zooplankton. In contrast with previous models, we use a non-monotonic functional response to capture the TPP group defense effect wherein zooplankton predation decreases at high TPP density. We look at the effects of TPP group defense and toxin liberation delay (TLD) in the rapid onset and offset of HABs. We derive sufficient conditions for the local stability of possible equilibria depicting coexistence and mono-species bloom resulting in HAB. Our simulations observe solutions converging to either, depending on the initial history. We then show that varying the TLD can destabilize such coexistence via Hopf bifurcation. Our numerical continuation illustrates branches of periodic solutions with stability information emerging from the Hopf bifurcations. The results provide insights into the dynamic behavior of both plankton species and recurring HABs worldwide.