Multiple dynamics and Hamilton energy analysis of a simple chaotic and hyperchaotic 3D non-autonomous circuit

A structurally simple chaotic and hyperchaotic 3D non-autonomous circuit is presented, which incorporates three dynamic components, an inductor, a capacitor, and an active first-order flux-controlled memristor, alongside a resistor and an independent voltage source. The circuit can be modeled in the voltage–current domain and flux–charge domain respectively. From the flux–charge domain, it is noted that by the introduction of periodic forces, the number and type of AC equilibrium points in the circuit system changes with time, facilitating more complex dynamic behaviors. From the voltage–current domain, numerous numerical simulation methods are employed to investigate the dynamic behaviors of the circuit system, such as phase diagrams, bifurcation diagrams, Lyapunov exponents, and 2-dimensional basins of attraction. The non-autonomous circuit system can give birth to multiple dynamic behaviors as the voltage source, component parameters, and the memristor’s initial state value changes. It can exhibit periodic cycles, chaos, hyperchaos, infinite coexisting attractors, extreme multistability, transient dynamics, and offset boosting behavior. Moreover, Hamilton energy function and its derivative are utilized to analyze of the dynamic characteristics for nondimensional system corresponding to the non-autonomous circuit, from the perspective of energy dissipation and generation. Additionally, the circuit implementation through Multisim validates the findings of the theoretical analysis. The non-autonomous circuit, distinguished by its simple structure, exhibits multiple dynamics, paving a way for the applications in various engineering domains as weak signal detection and signal encryption.