Symmetry, chaos control and hysteresis in a second-order non-autonomous circuit with square-wave excitation

In this paper, we report the dynamical evolution of a second-order non-autonomous electronic circuit, namely, the Murali-Lakshmanan-Chua (MLC) circuit subjected to square wave excitation. The dynamics of the circuit is studied by varying the amplitude, duty cycle of the square wave and the DC offset voltage through phase-portraits, power spectrum, one-parameter bifurcation diagrams, Lyapunov exponents and two-phase diagrams. Experimentally observed oscilloscope images and power spectra are presented to confirm the numerical studies. With the amplitude, duty cycle of the square wave and DC offset voltage as control parameters, a rich variety of dynamical phenomena such as chaos, dynamical symmetry, hysteresis, period-doubling structures are observed and reported. Finally, analytical solutions are developed for the square wave forced system and the multistability behavior observed through numerical and experimental studies are validated using the analytical results.