Dynamic Analysis of a New Chaotic System with Multistability, Amplitude and Offset Boosting Control, Its Adaptive Synchronization

In the present work, a new 3D chaotic system is reported. The proposed system is constructed using five nonlinear terms and four parameters. The novelties of the new system are it can exhibit initial condition-oriented multiple coexisting attractors, amplitude control, and offset boosting control. Firstly, the basic behaviors of the system such as stability, and Lyapunov exponents are analyzed in detail. Then, the dynamical behavior of the system is analyzed using bifurcation diagrams and the Lyapunov spectrum. It is shown that the system experiences periodic and chaotic attractors by varying the system parameters in a particular region. It is also shown that the system can present multiple coexisting attractors by plotting the bifurcation diagram for different initial conditions. The amplitude and offset boosting control of the system are verified with the help of bifurcation plot and Lyapunov exponent plot. Rich chaotic dynamics are found for various system parameters. Finally, the nonlinear feedback adaptive controller is designed to synchronize the proposed system. The numerical simulations are performed to show the effectiveness of the designed control scheme.