Bursting oscillations and coexisting attractors in a simple memristor-capacitor-based chaotic circuit

The design and analysis of a simple autonomous memristive chaotic circuit are important in theoretical, numerical, and experimental demonstrations of complex dynamics. In this paper, a simple autonomous memristive circuit is implemented, which only consists of an active second-order memristive diode bridge and a capacitor. Based on the available circuit, the mathematical model is established and its symmetry, dissipativity, and equilibrium stability are analyzed. Numerical simulations show that the proposed circuit exhibits complex behaviors of unipolar periodic and chaotic bursting oscillations along with coexisting attractors. It is worth noting that the circuit exhibits such a special bursting behavior previously unobserved in third-order autonomous memristive circuits. Moreover, spectral entropy complexities are calculated to provide an intuitive and effectual method for the circuit parameter configurations. The circuit simulations and hardware experiments verify the theoretical analyses and numerical simulations.