Symmetrical Hopf-induced bursting and hyperchaos control in memristor-based circuit

In this paper, a simple chaotic memristor-based circuit with an external stimulation is proposed, and its basic dynamic properties are demonstrated. When the external perturbation becomes time varying and its frequency is low enough, the system has two-time scales, which can be employed to explore the mechanisms of symmetrical Hopf-induced bursting oscillations and delay effects. Furthermore, delay-times on Hopf-induced bursting at different frequencies of the external stimulation are measured. The results show that the relationship between the delay-time and external frequency is subject to a power law. In order to enhance the existing chaos of the system, a 4D system is developed by adding a nonlinear state feedback controller, which shows hyperchaos under some suitable parameters. These two systems are implemented on Multisim and hardware platforms, and the corresponding experimental results verify the correctness of the numerical simulations.