Dynamical behaviors, circuit design, and synchronization of a novel symmetric chaotic system with coexisting attractors

In this paper, we introduce a novel three-dimension chaotic system with strange characteristic by applying construction of a 3D chaotic circuit method. Multiple equilibria and abundant coexisting attractors exist in this system. A mathematical model is developed and detailed stability analyses for equilibrium points are executed with obtaining significant results of the period-doubling bifurcation patterns confirmed by phase plane plots and Lyapunov exponent spectra. By varying the initial value and unique controlled parameter, the double-scroll chaotic attractor is broken up into a pair of symmetric singular attractors. Then, the local basins of attraction are investigated concerning the initial condition. Next, the circuit synthesis results generated by Multisim simulation tool validate the self-excitation characteristics of this system. Finally, the feedback control technique is used to study difference synchronization of this system. Main conclusions prove the validity and reliability of difference synchronization.

Automated summary

In this paper, a novel three-dimensional chaotic system with strange characteristic is introduced by applying a construction method of a 3D chaotic circuit. The system exhibits multiple equilibria and abundant coexisting attractors. A mathematical model is developed and stability analyses for equilibrium points are conducted, yielding significant results of period-doubling bifurcation patterns confirmed by phase plane plots and Lyapunov exponent spectra. By varying the initial value and a unique controlled parameter, the double-scroll chaotic attractor is broken up into a pair of symmetric singular attractors. Furthermore, the local basins of attraction are investigated with respect to the initial condition. The circuit synthesis results generated by Multisim simulation tool validate the self-excitation characteristics of this system. Finally, the feedback control technique is utilized to study difference synchronization of this system, and the main conclusions confirm the validity and reliability of difference synchronization.