Infinitely Many Necklace-Shaped Coexisting Attractors in a Nonautonomous Memcapacitive Oscillator

Abstract

Extreme multistability usually emerges in a mem-element’s circuit or system that possesses a line or plane equilibrium set closely associated with the internal initial state of the mem-element. To extend the investigation of extreme multistability, this paper proposes a nonautonomous memcapacitive oscillator, discovering a new type of extreme multistability due to the infinitely many discrete equilibrium points therein. This memcapacitive oscillator is constructed by connecting a simple memcapacitor-resistor circuit with a sinusoidal voltage. With its normalized model, the infinitely many discrete equilibrium points are computed and the infinitely many necklace-shaped coexisting attractors that were not yet reported are disclosed by numerical methods. Since the number and stability of the equilibrium points vary with time, the attraction basins with complex ripple structures are formed in the memcapacitive oscillator, resulting in the appearance of a special type of extreme multistability. Furthermore, PSIM circuit simulations and microcontroller-based hardware experiments are performed to verify the numerical results.

Extreme Multistability and Its Incremental Integral Reconstruction in a Non-Autonomous Memcapacitive Oscillator

“…This is the main reason that extreme multistability is often discovered in some circuits and systems involving memory-circuit elements. Intriguingly, extreme multistability has also been discovered in some non-autonomous memristive circuits and systems that have time-varying equilibria [33][34][35][36]. For example, a non-autonomous memristive FitzHugh−Nagumo circuit with its equilibrium points transitioning between no equilibrium point and a line equilibrium set was built, and hidden extreme mulitstability was disclosed [34].…”

Energy computation and multistability in a class of second-order chaotic systems with simple nonlinearities: numerical, experimental and analytical results

“…Multistability is a situation in which a nonlinear system display several coexisting states for fixed set of system parameters but starting from different initial conditions [22,23]. Since its discovery by Arecchi et al [24], it has been reported in several biological [25], mechanical [26] and electronic [27] systems. Although no work up to date has clearly established its generation mechanism, various methods can be found throughout the literature for characterizing it.…”