A new three-dimensional chaotic system: its adaptive control and circuit design

Abstract

A new three-dimensional chaotic system with two nonlinearities is proposed in this research work. Specifically, the two nonlinearities considered in the construction of the new chaotic system are a quadratic nonlinearity and a quartic nonlinearity. A systematic study of the three-dimensional chaotic system has been made including phase portraits, dissipativity, rest points and their stability, Lyapunov chaos exponents, Kaplan-Yorke fractal dimension, etc. As main control results, we design feedback control laws using adaptive control theory to achieve global stabilisation of the new chaotic system and also global synchronisation of identical chaotic systems with unknown parameters. Finally, an electronic circuit design of the new chaotic system using electronic work bench (EWB) is described in detail to confirm the feasibility of the theoretical chaotic model.