Math. Model. Nat. Phenom.
Volume 3, Number 4, 2008Patterns and waves in ecology and evolution (2)
|Page(s)||71 - 95|
|Published online||04 December 2008|
Wave of Chaos and Pattern Formation in Spatial Predator-Prey Systems with Holling Type IV Predator Response
Department of Applied Mathematics,
Indian School of Mines University, Dhanbad 826 004,
2 Centre for Biomedical Engineering, Indian Institute of Technology New Delhi, Hauz Khas, Delhi 110 016, India
Corresponding author: email@example.com
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. Type IV functional response yields to type II response in the event of large immunity from or tolerance of prey. It has been found that the Wave of Chaos (WoC) is still effective mechanism for the propagation of chaotic dynamics in predation and competitive systems. Fish predation has a significant role in the temporal evolution of spatial patterns of phytoplankton-zooplankton system. From a field ecologist's perspective, it is not only important to know the stable stationary patterns of an evolving phytoplankton-zooplankton system, but also to know at what point of time these observations are carried out. This has implications for ecological theory.
Mathematics Subject Classification: 35K57 / 37D45
Key words: spatial predator-prey system / hopf-bifurcation / reaction-diffusion / pattern formation
© EDP Sciences, 2008
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