The Rich Dynamics of Memristive Devices with Non-Separable Nonlinear Response

In this brief, we classify the instantaneous response of resistors with memory into three types: linear (L), separable nonlinear (SN), and non-separable nonlinear (NSN). A particular model of an NSN-type memristive device is introduced and used to demonstrate the possibility of rich dynamics in the memristor-capacitor circuit subjected to a sinusoidal voltage. In particular, our numerical simulations reveal the regimes of double period oscillations, multiple period oscillations, and chaotic oscillations. The comparison with L-type and SN-type memristive devices described by the same differential state equation indicates the importance of the NSN-type response to achieve such complex dynamics in the memristor-capacitor circuit with a first-order memristive device. Moreover, we demonstrate that a compound NSN-type memristive device can be assembled using one L-type memristive device, two resistors, and two diodes. The complex behavior of such compound devices is verified using SPICE modeling.