Analysis, control, synchronization, and circuit design of a novel chaotic system

This article introduces a novel three-dimensional autonomous chaotic system with a single cubic nonlinearity. Several issues, such as the basic dynamical behaviour, equilibria, Lyapunov exponent spectrum, and bifurcations of the new chaotic system, are investigated analytically and numerically. Next, adaptive control laws are designed to stabilize the new chaotic system with unknown parameters to its unstable equilibrium point at the origin, based on adaptive control theory and Lyapunov stability theory. Then, adaptive control laws are derived to achieve global chaos synchronization of identical new chaotic systems with unknown parameters. Further to these, a novel electronic circuit realization of the proposed chaotic system is presented and examined using the Orcad-PSpice® program. It is convenient to use the new chaotic system to purposefully generate chaos in chaos applications. A good qualitative agreement is shown between the simulations and the experimental results.