Complex Dynamics in a Memcapacitor-Based Circuit

Abstract

In this paper, a new memcapacitor model and its corresponding circuit emulator are proposed, based on which, a chaotic oscillator is designed and the system dynamic characteristics are investigated, both analytically and experimentally. Extreme multistability and coexisting attractors are observed in this complex system. The basins of attraction, multistability, bifurcations, Lyapunov exponents, and initial-condition-triggered similar bifurcation are analyzed. Finally, the memcapacitor-based chaotic oscillator is realized via circuit implementation with experimental results presented.

A Nonvolatile Fractional Order Memristor Model and Its Complex Dynamics

“…According to Equation (23), the eigenvalues of the system at the equilibrium point w = 0 can be calculated as λ 1 = 2.3207, λ 2,3 = −1.0603 ± 2.3658, and λ 4 = 0. Taking α = 0.99, we obtain απ/2 = 1.551 and arg(λ i ) = 0, i.e., arg(λ i ) < απ/2, which meets the stability criterion of Equation (24). The distribution of eigenvalues on the complex plane is shown in Figure 8, from which we observe that the points corresponding to eigenvalue λ 1 = 2.3207 are in the unstable region.…”

“…Taking α = 0.99 and (x(0), y(0), z(0), w(0)) = (0, 0, 0.001, 0), the attractor trajectory of the system in the x-z phase plane is shown in Figure 9. The corresponding Lyapunov exponents [44] , which meets the stability criterion of Equation (24). The distribution of eigenvalues on the complex plane is shown in Figure 8, from which we observe that the points corresponding to eigenvalue λ = Table 1 lists the circuit dynamics with equilibrium parameter w, eigenvalues, and fractional order α.…”

“…There are many complex dynamic phenomena in chaotic systems, such as coexisting bifurcation, coexisting attractors, hidden attractors, multi-stability, etc. Reference [24] analyzed the complex dynamics in a memcapacitor-based circuit. Reference [25] proposed a memristive wien-bridge chaotic circuit, and the coexisting attractors and multi-stability of chaotic systems were analyzed in these two references.…”

Unstable Limit Cycles and Singular Attractors in a Two-Dimensional Memristor-Based Dynamic System

“…Coexistence of attractors is often observed in higher-dimensional nonlinear autonomous dynamical systems [ 26 , 27 , 28 ] or a two-dimensional nonlinear non-autonomous system [ 29 ]. For two-dimensional autonomous systems, however, this phenomenon is generally not possible.…”

Coexisting Attractors and Multistability in a Simple Memristive Wien-Bridge Chaotic Circuit

“…A Wien-bridge chaotic oscillator based on an SBT memristor was designed in Reference [22]. Besides, some dynamical behaviors in chaotic systems were analyzed with the help of a phase diagram, Poincare section, bifurcation diagram, and Lyapunov exponent spectrum [23][24][25]. Specifically, coexisting attractors and multistability are common phenomena in a chaotic system, which indicates that a chaotic system with fixed parameters under different initial conditions can generate disparate attractors.…”