Stability and Bifurcation for a Delayed Diffusive Two‐Zooplankton One‐Phytoplankton Model with Two Different Functions

Abstract

In this paper, a diffusion two-phytoplankton one-zooplankton model with time delay, Beddington–DeAnglis functional response, and Holling II functional response is proposed. First, the existence and local stability of all equilibria of such model are studied. Then, the existence of Hopf bifurcation of the corresponding model without diffusion is given by taking time delay as the bifurcation parameter. Next, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are investigated by using the normal form theory and center manifold theorem. Furthermore, due to the local bifurcation theory of partial functional differential equations, Hopf bifurcation of the model is investigated by considering time delay as the bifurcation parameter. The explicit formulas to determine the properties of Hopf bifurcation are given by the method of the normal form theory and center manifold theorem for partial functional differential equations. Finally, some numerical simulations are performed to check out our theoretical results.

Stability analysis of the depletion of dissolved oxygen for the Phytoplankton-Zooplankton model in an aquatic environment

“…Plankton dynamics research is a fascinating field of study. Plankton constitutes the building elements of all aquatic food chains with phytoplankton occupying the first trophic level [17]. Toxins are produced by phytoplankton which serves an essential environmental function and cannot be ignored.…”