Stability, Chaos and Estimation of the Unknown Parameters of Habitat Destruction Model with Prey-Predator-Top Predator

Abstract

This paper is devoted to study the problem of stability, chaos behavior and parameters estimation of the habitat destruction model with three-species (prey, predator and top-predator). The mathematical formula of the model and its proposed interactions are presented. Some important special solutions of systems are discussed. The stationary states of the model are derived. Local stability conditions for the stationary states are derived. Furthermore, the chaotic behavior of the model is discussed and presented graphically. Using Liapunov stability technique, the dynamic estimators of the unknown probabilities and their updating rules are derived. It is found that, the control laws are non-linear functions of the species densities. Numerical illustrative examples are carried out and presented graphically.