Chaotic dynamics of a three species prey–predator competition model with noise in ecology

Abstract

In this paper we investigate a three species ecosystem consisting of a prey, a predator and a top predator. The predator survives on the prey and the top predator survives on both the prey and the predator. The mathematical model consists of non-linear simultaneous differential equations. All the eight equilibrium points of the model are identified and by using Routh–Hurwitz criteria as well as Lyapunov function, we derive the criteria for local and global stabilities. Also the population intensities of fluctuations (variances) around the positive equilibrium due to noise are computed; their stability is also analyzed with computer simulation using Matlab. Some Numerical simulations for justifying the theoretical analysis are also provided. The main conclusions are supplied in conclusion.