A new 4D Bouali chaotic system: Analysis, control and circuit implementation

The dynamical system has been widely studied. A novel Bouali Four-Dimension Continuous time dynamical system is constructed from Three Dimension continuous time Bouali System by adding one more variable and their associated equation represent, the interactions between the new variable and the original ones. The fundamental properties such as equilibrium points and its stability, dissipativity, multistability, waveform and phase space, state space analysis, Lyapunov exponents and Lyapunov dimension are studied. The analysis's findings indicate that the new Bouali system is unstable and hyper chaotic with fractal dimension (Kaplan Yorkdim) dimension Dky=3.249. A novel feature of the new Chaotic system has multistability and coexistence attractor for two different sets of initial conditions. Adaptive Control and Synchronization system has been created; it is found the hyperchaotic new Bouali system achieved good results. Finally, the implementation of electronic circuit is designed through Multisim 14.2 software, for the new hyperchaotic system, showed agreement with numerical simulation results from MATLAB 2024 which confirming from with the validity and effectiveness of the new system, and useful for practical engineering realization.