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Computational Ecology and Software, 2012, 2(1): 1-25
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Spatiotemporal pattern induced by self and cross-diffusion in a spatial Holling-Tanner model

Ranjit Kumar Upadhyay, N. K. Thakur
Department of Applied Mathematics, Indian School of Mines, Dhanbad 826004, India

Received 26 July 2011;Accepted 30 August 2011;Published online 1 March 2012
IAEES

Abstract
In this paper, we have made an attempt to provide a unified framework to understand the complex spatiotemporal patterns induced by self and cross diffusion in a spatial Holling-Tanner model for phytoplankton-zooplankton-fish interaction. The effect of critical wave length which can drive the system to instability is investigated. We have examined the criterion between two cross-diffusivity (constant and timevarying) on the stability of the model system and for diffusive instability to occur. Based on these conditions and by performing a series of extensive simulations, we observed the irregular patterns, stationary strips, spots, and strips-spots mixture patterns. Numerical simulation results reveal that the regular strip-spot mixture patterns prevail over the whole domain on increasing the values of self- diffusion coefficients of phytoplankton and zooplankton and the dynamics of the system do not undergo any further changes.

Keywords spatiotemporal pattern;diffusion;Holling-Tanner model;phytoplankton-zooplankton-fish interaction.

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