The prediction of the behavior of the chaotic dynamical systems is so difficult due to their extreme sensitivity to any change in the initial values of their conditions. However, the prediction of any system development is a very important goal. The present paper aimed to discuss the coupled dynamical system of Lorenz-Rössler in terms of the local stability analysis and the mathematical approximation of the undefined parameters. Using the linear stability analysis logic, it is found that under some conditions, the system is dispersed dissipative and unstable at equilibrium . The estimators of the undefined parameters and their updating functions are obtained by using the Lyaponouv technique and the asymptotic stability conditions. It is shown there is a strong converging to the assumed values over time. Some arithmetic solutions for the unrestrained model and its chaotic performance are shown by graphics. Some examples for our estimators of the undefined parameters and the behavior of its updating rules are also graphically presented. The percentage of errors (PEs) in the estimation process are calculated. Finally, some special cases of the assumed model are presented and discussed.
Volume 12 | 08-Special Issue
Pages: 951-961
DOI: 10.5373/JARDCS/V12SP8/20202600