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.
Highlights
The habitat destruction is very important topic, which has received considerable attention in the last years
This paper is devoted to study the problem of stability, chaos behavior and parameters estimation of the habitat destruction model with three-species
The dynamic estimators of the unknown parameters and its updating rules over time are derived from the conditions of the asymptotic stability of the system around its steady states
Summary
The habitat destruction is very important topic, which has received considerable attention in the last years. When the habitat is no longer able to provide appropriate conditions for the life of its organisms, we can say that, the environment reached to the destruction stage, which is considered as an important factor causing extinction. It effects on various species directly and indirectly. Alwan has studied the stability and behavior for the model of stochastic lattice gas of prey-predator model with pair-approximation She found that this system has a chaos behavior and she has derived the estimators of the unknown parame-.
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