Stability Analysis and Chaotic Behavior of the Classical R?ssler System Using Simulated EEG Signals

The study and analysis of dynamical is currently important, especially in applied fields. The research presents a numerical and analytical study of the classical model for under standing the dynamic behavior of the suggested a three dimensional biomathematical autonomous system, which made up of three ordinary equations, that represent the model variables. The dynamic properties of the suggested system are verified by equilibrium points and its stability such as the roots of the characteristic equation, Routh-Hurwitz criteria, and Lyapunov function, dissipativity, bifurcation and Kaplan-York dimension. Simultaneously, the system parameters were estimated using genetic algorithm based on real EEG data to improve the models fit to the target data. All simulations were performed using MATLAB and R-K4 numerical method. The 0 - 1 test was applied to simulated system data and real EEG data, and the results were compared, the comparison showed similar characteristic in both cases confirming and supporting the system’s ability to represented complex biological data. The results indicate the system’s efficiency as an effective tools. Showed EEG system is unstable and chaotic biological system.