Dynamical analysis of chaotic circuits with computational algebra method

This study analyses a novel autonomous non- linear continuous-time system derived from Bao's simple third-order inductor-free memristive chaotic circuit for chaotic dynamics via computer algebra. Bao et al. designed the Chua memristor emulator with resistors, capacitors, and opamps to avoid the negative effects of the inductor [1]. This simple third-order inductor-free chaotic circuit utilizes reasonably functional discrete components, which are significant with the number of dynamically simplified elements for mathematical representation of chaotic behaviour. Our proposed model aims to overcome the negative long-term effects on the electrical properties of the capacitor and reveal experimental results depending on an additional variable that behaves like an electrical inductor. Numerical examples are given to study bifurcation properties in the modified chaotic circuit concerning the results with Lyapunov regimes and also to identify limit cycles of period-1, period-2, period-4, and chaotic attractors in the proposed circuit.