Hidden chaotic mechanisms for a family of chameleon systems

Abstract

Chameleon chaotic systems are nonlinear dynamical systems whose chaotic attractors can transform between hidden and self-excited types by tuning system parameters to modify equilibrium points. This paper proposes a novel family of chameleon chaotic systems, which can exhibit three types of chaotic attractors: self-excited attractors with a nonhyperbolic equilibrium, hidden attractors with a stable equilibrium, and hidden attractors with no equilibrium points. Bifurcation analysis uncovers the mechanisms by which self-excited and hidden chaotic attractors arise in this family of chameleon systems. It is demonstrated that various forms of chaos emerge through period-doubling routes associated with changes in the coefficient of a linear term. An electronic circuit is designed and simulated in Multisim to realize a hidden chaotic system with no equilibrium points. It is demonstrated that the electronic circuit simulation is consistent with the theoretical model. This research has the potential to enhance our comprehension of chaotic attractors, especially the hidden chaotic attractors.

Keywords

• hopf bifurcation
• period-doubling route
• bifurcation diagram
• hidden chaotic attractor