Hidden multistability in four fractional-order memristive, meminductive and memcapacitive chaotic systems with bursting and boosting phenomena

The operation of memristive, meminductive and memcapacitive circuit components depend on their history of devices, i.e. they are memory dependent. This paper proposes new fractional-order (FO) models of four such circuits since FO derivative is calculated using the past history of time and helps in understanding the memory-dependent dynamics of these memory devices better as compared to the integral derivative. Interestingly, these fractional-order memristive, meminductive and memcapacitive systems (FOMMMSs) display a myriad of dynamics such as ranging from coexisting to hidden attractors, chaotic to hyperchaotic attractors, periodic orbits to stable foci, bursting oscillations transitioning from chaos to periodic states and vice versa, offset boosting phenomenon, and a varied nature of infinite equilibria. The proposed fractional-order systems can have a number of applications such as in oscillator circuits, and secure communication due to the increased randomness of hidden multistability. The theoretical analyses of existence of multistability and hidden attractors in the proposed FOMMMSs comply with that of the numerical simulation and circuit implementation results.

Automated summary

This paper introduces new fractional-order models for explaining the dynamics of memory-dependent memristive, meminductive, and memcapacitive systems, showing various dynamic behaviors including chaos, periodicity, bursting oscillations, etc. These fractional-order systems have broad applications, such as in oscillator circuits and secure communication.