Abstract
Extreme multistability has frequently been reported in autonomous circuits involving memory-circuit elements, since these circuits possess line/plane equilibrium sets. However, this special phenomenon has rarely been discovered in non-autonomous circuits. Luckily, extreme multistability is found in a simple non-autonomous memcapacitive oscillator in this paper. The oscillator only contains a memcapacitor, a linear resistor, a linear inductor, and a sinusoidal voltage source, which are connected in series. The memcapacitive system model is firstly built for further study. The equilibrium points of the memcapacitive system evolve between a no equilibrium point and a line equilibrium set with the change in time. This gives rise to the emergence of extreme multistability, but the forming mechanism is not clear. Thus, the incremental integral method is employed to reconstruct the memcapacitive system. In the newly reconstructed system, the number and stability of the equilibrium points have complex time-varying characteristics due to the presence of fold bifurcation. Furthermore, the forming mechanism of the extreme multistability is further explained. Note that the initial conditions of the original memcapacitive system are mapped onto the controlling parameters of the newly reconstructed system. This makes it possible to achieve precise control of the extreme multistability. Furthermore, an analog circuit is designed for the reconstructed system, and then PSIM circuit simulations are performed to verify the numerical results.
Highlights
Memory-circuit elements can be traced back to the 1971 [1], but the field gained considerable momentum after the first physical realization of a memristive device, which was implemented by Struckov et al at Hewlett-Packard [2]
Extreme multistability with the coexistence of infinitely many attractors [24–28] has attracted scientists’ attention. This special phenomenon is frequently discovered in autonomous circuits and systems involving memory-circuit elements, since these circuits and systems have line or plane equilibrium sets [14,29–32]
The stabilities of the equilibrium sets are determined by the initial conditions of memory-circuit elements, which induces the coexistence of infinitely many attractors
Summary
Memory-circuit elements can be traced back to the 1971 [1], but the field gained considerable momentum after the first physical realization of a memristive device, which was implemented by Struckov et al at Hewlett-Packard [2]. Extreme multistability with the coexistence of infinitely many attractors [24–28] has attracted scientists’ attention This special phenomenon is frequently discovered in autonomous circuits and systems involving memory-circuit elements, since these circuits and systems have line or plane equilibrium sets [14,29–32]. The stabilities of the equilibrium sets are determined by the initial conditions of memory-circuit elements, which induces the coexistence of infinitely many attractors This is the main reason that extreme multistability is often discovered in some circuits and systems involving memory-circuit elements. This simple circuit is only composed of one resistor, one inductor, one ideal memcapacitor, and one sinusoidal voltage source.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
