A New Chaotic System With Stable Equilibrium: From Theoretical Model to Circuit Implementation

Recent evidences suggest that complex behavior such as chaos can be observed in a nonlinear system with stable equilibria. However, few studies have investigated chaotic systems with only one stable equilibrium. This paper introduces a new 3-D chaotic system having only one stable equilibrium. Dynamics of the new system are discovered by using phase portraits, basin of attraction, bifurcation diagram, and maximal Lyapunov exponents. It is interesting that the system has a state variable related with the freedom of offset boosting. In addition, we have investigated the anti-synchronization of the system via an adaptive control. Furthermore, the feasibility of the system is also discussed through presenting its electronic circuit implementation.