Dynamics of an Amplitude-Modulated Memristive Circuit: A Study of Periodic and Chaotic Regimes

Abstract

This study investigates the periodic and chaotic dynamics of an amplitude-modulated (AM) memristive circuit using numerical simulations based on the fourth-order Runge-Kutta method. The system’s response is analyzed under varying modulation parameters, revealing a rich spectrum of nonlinear phenomena, including period-doubling and reverse period-doubling bifurcations, period-bubbling, quasiperiodic oscillations, and chaotic behavior. Bifurcation diagrams, phase portraits, and Poincar’e sections confirm the presence of chaotic attractors and complex dynamical regimes. The frequency and amplitude of the modulating signal play a pivotal role in shaping the system’s behavior, influencing both the onset of chaos and the structure of the resulting attractors. Furthermore, the memristive nature of the circuit is verified through the presence of pinched hysteresis loops in the voltage-current (v - i) characteristics-an essential signature of memristive systems. These loops exhibit distinct frequency- and amplitude-dependent variations, underscoring the nonlinear, memory-dependent behavior inherent to the memristor.