Abstract
In this paper, the problem of chaos, stability and estimation of unknown parameters of the stochastic lattice gas for prey-predator model with pair-approximation is studied. The result shows that this dynamical system exhibits an oscillatory behavior of the population densities of prey and predator. Using Liapunov stability technique, the estimators of the unknown probabilities are derived, and also the updating rules for stability around its steady states are derived. Furthermore the feedback control law has been as non-linear functions of the population densities. Numerical simulation study is presented graphically.
Highlights
A lattice model usually represents the motion of a network of particles, where the motion is produced by forces acting between the neighboring particles
El-Gohary has studied the problems of chaos and optimal control cancer model with complete unknown parameters [9]
This paper is considered as an extension of the paper [15] where it will discuss the stability and estimation of the unknown parameters of the stochastic lattice gas model for prey-predator when two-site approximation is used
Summary
A lattice model usually represents the motion of a network of particles, where the motion is produced by forces acting between the neighboring particles. El-Gohary has studied the problems of chaos and optimal control cancer model with complete unknown parameters [9]. El-Gohary and Alwan have discussed the problem of chaos and control of a stochastic lattice gas model for preypredator when one-site approximation is used. They have studied stability of the system and derived the optimal control inputs. This paper is considered as an extension of the paper [15] where it will discuss the stability and estimation of the unknown parameters of the stochastic lattice gas model for prey-predator when two-site approximation is used.
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