Population Dynamics and Pattern Formation in a Plankton Model

We study a spatio–temporal prey–predator model of plankton. This model has spatial interaction terms, which has the DeAngelis-Beddington functional response, to describe the grazing pressure of microzooplankton (M) on phytoplankton (P) is controlled through external info–chemical (C) mediated predation by copepods (Z). The Beddington DeAngelis functional response plays a critical role in modeling plankton. It is an advance on the prey-dependent Holling's type II functional response. It can be used to explain the predators' per capita feeding rates on prey. This functional response can also be used to provide better descriptions of predator prey abundances and how these affect predator feeding, discussed that in their predator prey system, Beddington DeAngelis was used to describe mutual interference by predators within the ecosystem. In relation to this, the concept was used to highlight the effect of changes in prey density on the predator density attached per unit time.The Beddington DeAngelis functional response can be used to perform a detailed mathematical analysis of the intra-specific competition among predators. We undertake a stability analysis of the two species model and compare the system dynamics. In relation to this, the critical conditions for Kinesis are derived; these are necessary and sufficient.