Control and Synchronization of a Novel Realizable Nonlinear Chaotic System

The study proposes a novel chaotic system with a cubic non-linear term. Different system characteristics are investigated including equilibria, stability, invariance, dissipation, Lyapunov dimension, and Lyapunov exponents. Also, the electronic circuit and Signal flow graph of the system are carried out to show the applicability of the chaotic system. Lyapunov stability theorem converts the system's chaotic behavior to unstable trivial fixed point. The study also focuses on demonstrating complete synchronization between two similar novel chaotic systems. According to Lyapunov stability theorem, simple application in secure communication was developed by employing the chaos synchronization results. Numerical simulations for the systems are performed for establishing the synchronization strategy effectiveness and proposed control.

Automated summary

The study proposes a new chaotic system with a cubic non-linear term and investigates various characteristics of the system such as equilibria, stability, invariance, dissipation, Lyapunov dimension, and Lyapunov exponents. The electronic circuit and signal flow graph are implemented to demonstrate the applicability of the chaotic system. The study also focuses on achieving complete synchronization between two similar novel chaotic systems and applying it in secure communication using Lyapunov stability theorem.