Hyperchaos, quasi-period and coexisting behaviors in second-order-memristor-based jerk circuit

This paper generalizes a second-order-memristor-based jerk circuit, which is achieved by substituting the first-order memristor contained diode-bridge and RC filter in an existing memristive jerk circuit with a second-order one composed of diode-bridge and LC network. The second-order-memristor-based jerk circuit possesses an unstable saddle-focus and generates complex parameter-dependent dynamics, including hyperchaos, chaos, quasi-period, and period along with coexisting behaviors. The coexistences of symmetric chaotic and quasi-periodic attractors are shown by local attraction basins. Particularly, 2D two-layer-based dynamical maps on the system parameter spaces are employed to perfectly detect complex dynamical behaviors of hyperchaos and quasi-period. Furthermore, hardware breadboard is made for experimental investigations and the measurement results well validate complex parameter-dependent dynamics revealed by the numerical simulations.