Bifurcations in a Patch-forming Plankton Model with Toxin Liberation Delay

JuanchoCollera

University of the Philippines Baguio

"Bifurcations in a Patch-forming Plankton Model with Toxin Liberation Delay"

Harmful algal blooms (HABs) are characterized by rapid growth of algae, and can be caused by toxin-producing phytoplankton (TPP). When HABs occur, oxygen in the water depletes and thus can kill fish and other marine creatures causing both environmental and economic damages. In this talk, we consider a zooplankton-phytoplankton model under the assumption that the TPP exhibits group defense so that zooplankton predation decreases at high TPP density. Furthermore, we assume that toxin liberation by the TPP is not instantaneous but is rather mediated by a time lag, which is also known as the toxin liberation delay (TLD). Our results show that the model system undergoes a Hopf bifurcation around a coexistence equilibrium when the value of the TLD reaches a certain threshold. For values of the TLD just above the threshold, the stable limit cycle that is created depicts the manageable periodic fluctuation of the populations. However, when the value of the TLD is increased further, recurring blooms of various periodicity were observed which can be attributed to the occurrence of period-doubling bifurcations.
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