Table of Contents
ISRN Biomathematics
Volume 2013 (2013), Article ID 198185, 12 pages
http://dx.doi.org/10.1155/2013/198185
Research Article

Pattern Formation in Spatially Extended Tritrophic Food Chain Model Systems: Generalist versus Specialist Top Predator

School of Basic Sciences, Indian Institute of Technology Mandi, Mandi, Himachal Pradesh 175 001, India

Received 20 November 2012; Accepted 11 December 2012

Academic Editors: M. T. Figge and A. A. Polezhaev

Copyright © 2013 Nitu Kumari. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The complex dynamics of two types of tritrophic food chain model systems when the species undergo spatial movements, modeling two real situations of marine ecosystem, are investigated in this study analytically and using numerical simulations. The study has been carried out with the objective to explore and compare the competitive effects of fish and molluscs species being the top predators, when phytoplankton and zooplankton species are undergoing spatial movements in the subsurface water. Reaction diffusion systems have been used to represent temporal evolution and spatial interaction among the species. The two model systems differ in an essential way that the top predators are generalist and specialist, respectively, in two models. “Wave of Chaos” mechanism is found to be the responsible factor for the pattern (non-Turing) formation in one dimension seen in the food chain ending with top generalist predator. In the present work we have reported WOC phenomenon, for the first time in the literature, in a three-species spatially extended food chain model system. The numerical simulation leads to spontaneous and interesting pattern formation in two dimensions. Constraints on different parameters under which Turing and non-Turing patterns may be observed are obtained analytically. Diffusion-driven analysis is carried out, and the effect of diffusion on the chaotic dynamics of the model systems is studied. The existence of chaotic attractor and long-term chaotic behavior demonstrate the effect of diffusion on the dynamics of the model systems. It is observed from numerical study that food chain model system with top predator as generalist has very rich dynamics and shows very interesting patterns. An ecosystem having top predator as specialist leads to the stability of the system.