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.
Highlights
The interest in the study of chaos in ecological systems has increased in the last couple of decades
After a detailed analytical and numerical simulation of model systems 1 and 2, in both one and two dimensions, we found that the spatially extended food chain model systems displayed chaotic dynamics leading to interesting spatial patterns
The present study reveals that top specialist predators like fish can stabilize the dynamics of the marine ecosystem
Summary
The interest in the study of chaos in ecological systems has increased in the last couple of decades. Interactions of population in ecological systems are modeled by continuous time models and have been studied extensively in the literature [1]. Diffusion equations have been used effectively to describe the movement of numerous animals in mark-recapture studies [2, 3] Another aspect of reaction-diffusion theory that has excited numerous applied mathematicians is the realization that adding diffusion to certain types of multispecies interactions will cause striking spatial patterns to emerge even in homogeneous environments [4]. Two types of aquatic food chain model systems are studied in the presence of diffusion in the present paper. The objective of this work is to investigate the effects of spatial interaction in marine ecosystem when top predator is either specialist or generalist in two different food chains.
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