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Wave of Chaos and Pattern Formation in Spatial Predator-Prey Systems with Holling Type IV Predator Response

R. K. UpadhyayN. KumariV. Rai — 2008

Mathematical Modelling of Natural Phenomena

The challenges to live in the open water and the diversity of habitats in the marine environments prompts phytoplankton to devise strategies which often involve production of toxins by Harmful Algal Bloom (HAB) and rapid production of metabolites from non-toxic precursor. The functional response of the predator is described by Holling type IV. We investigate wave phenomena and non-linear non-equilibrium pattern formation in a phytoplankton-zooplankton system with Holling type IV functional response....

Spatiotemporal Dynamics in a Spatial Plankton System

R. K. UpadhyayW. WangN. K. Thakur — 2010

Mathematical Modelling of Natural Phenomena

In this paper, we investigate the complex dynamics of a spatial plankton-fish system with Holling type III functional responses. We have carried out the analytical study for both one and two dimensional system in details and found out a condition for diffusive instability of a locally stable equilibrium. Furthermore, we present a theoretical analysis of processes of pattern formation that involves organism distribution and their interaction of spatially...

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