Complex behaviour in four species food-web model

Abstract

A four-dimensional food-web system consisting of a bottom prey, two middle predators and a generalist predator has been developed with modified functional response. The system is well posed and dissipative. Some results on uniform persistence have been developed. The dynamics of the system is found to be chaotic for certain choice of parameters. The coexistence of all four species is possible in the form of periodic orbits/strange attractors for suitably chosen set of parameters.

Hopf Bifurcation, Hopf-Hopf Bifurcation, and Period-Doubling Bifurcation in a Four-Species Food Web

“…Currently, research on food web dynamics slipped into the cases where four species or more species exist and interact [2,12,13]. Rich dynamic behaviors of four-species or more species food webs, such as equilibria, bifurcations, periodic orbits, torus, chaotic attractors, and so on, have been found to be contributing to better comprehending on the complexity of species coexistence and community stability.…”

“…Rich dynamic behaviors of four-species or more species food webs, such as equilibria, bifurcations, periodic orbits, torus, chaotic attractors, and so on, have been found to be contributing to better comprehending on the complexity of species coexistence and community stability. In Gakkhar et al [2], a four-species food web model was developed and complex dynamic behaviors including strange attractor and chaos were shown. In the food web studied by Wei [13], Wei proved that the food web system possesses a line segment of degenerate steady states for the parameter values on a bifurcation line in the bifurcation diagram and found diverse routes to chaos.…”

“…After that, the food webs have been widely studied in various aspects of characteristics, involving stability, complexity, dynamics, etc. Via analyzing the characteristics of food webs, many research works have played an important role in understanding the properties of natural ecosystems [2][3][4].…”

Stability analysis of a complex four species food-web model

“…which is a natural enemy to the concerned prey and predators. A small number of models consisting of four species have been proposed and studied in the ecological literature [3,4,7,16]. The present article deals with the dynamical study of the underlying four species 'prey-two predators-superpedator' model.…”