Multiple attractors can be found in many nonlinear dynamical system with multistability. Recently, experimental attractors with two stable saddle-foci were reported to find in a non-ideal active voltage-controlled memristor based Chua's circuit. In this paper we focus on the multiple attractors found in the proposed memristive Chua's circuit. Concretely, by numerical simulations of mathematical model, hardware circuit experiments and PSIM circuit simulations, multiple attractors with different initial states are revealed and with the dimensionless system equations, complex dynamics with different initial conditions are further discussed. Theoretical derivation results indicate that the normalized memristive Chua's system has two stable nonzero saddle-foci in globally adjusting normalized parameter region and exhibits the unusual and striking dynamical behavior of multiple attractors with multistability.

Multiple attractors in a non-ideal active voltage-controlled memristor based Chua's circuit

This brief introduces a new floating memristor emulator circuit based on second-generation current conveyors and passive elements. A mathematical model to characterize the memristor behavior was derived, showing a good accuracy among HSPICE simulations and experimental results. An analysis of the frequency behavior of the memristor is also described, showing that the frequency-dependent pinched hysteresis loop in the current-versus-voltage plane holds up to 20.2 kHz. Theoretical derivations and related results are experimentally validated through implementations from commercially available devices, and the proposed memristor emulator circuit can easily be reproducible at a low cost. Furthermore, the emulator circuit can be used as a teaching aid and for future applications with memristors, such as sensors, cellular neural networks, chaotic systems, programmable analog circuits, and nonvolatile memory devices.

A Floating Analog Memristor Emulator Circuit

This paper presents an inductor-free memristive circuit, which is implemented by linearly coupling an active band-pass filter (BPF) with a parallel memristor and capacitor filter. Mathematical model is established, and numerical simulations are performed. The results verified by hardware experiments show that the active BPF-based memristive circuit exhibits the dynamical behaviors of point, period, chaos, and period-doubling bifurcation route. Most important of all, the newly proposed memristive circuit has a line equilibrium and its stability closely relies on memristor initial condition, which results in the emergence of extreme multistability. Stability distribution related to memristor initial condition is numerically estimated and the coexistence of infinitely many attractors is intuitively captured by numerical simulations and PSIM circuit simulations.

Coexisting infinitely many attractors in active band-pass filter-based memristive circuit

In this contribution, a novel memristor-based oscillator, obtained from Shinriki's circuit by substituting the nonlinear positive conductance with a first order memristive diode bridge, is introduced. The model is described by a continuous time four-dimensional autonomous system with smooth nonlinearities. The basic dynamical properties of the system are investigated including equilibria and stability, phase portraits, frequency spectra, bifurcation diagrams, and Lyapunov exponents' spectrum. It is found that in addition to the classical period-doubling and symmetry restoring crisis scenarios reported in the original circuit, the memristor-based oscillator experiences the unusual and striking feature of multiple attractors (i.e., coexistence of a pair of asymmetric periodic attractors with a pair of asymmetric chaotic ones) over a broad range of circuit parameters. Results of theoretical analyses are verified by laboratory experimental measurements.

Periodicity, chaos, and multiple attractors in a memristor-based Shinriki's circuit.

Design and implementation of a simple dynamical 4-D chaotic circuit with applications in image encryption

In this paper, a practical equivalent circuit of an active flux-controlled memristor characterized by smooth piecewise-quadratic nonlinearity is designed and an experimental chaotic memristive circuit is implemented. The chaotic memristive circuit has an equilibrium set and its stability is dependent on the initial state of the memristor. The initial state-dependent and the circuit parameter-dependent dynamics of the chaotic memristive circuit are investigated via phase portraits, bifurcation diagrams and Lyapunov exponents. Both experimental and simulation results validate the proposed equivalent circuit realization of the active flux-controlled memristor.

https://iopscience.iop.org/article/10.1088/1674-1056/20/12/120502/pdf

Chaotic memristive circuit: equivalent circuit realization and dynamical analysis

Study of the Game Model of E-Commerce Information Sharing in an Agricultural Product Supply Chain based on fuzzy big data and LSGDM

The dynamical behaviours of valley current controlled buck converter are studied by establishing its corresponding discrete iterative map model in this paper. Time-domain waveforms and phase portraits of valley current controlled buck converter are obtained by Runge–Kutta algorithm through a piecewise smooth switching model. The research results indicate that the valley current controlled buck converter exhibits rich nonlinear phenomena, and it has routes to chaos through period-doubling bifurcation and border-collision bifurcation in a wide parameter range. Interesting inverse nonlinear behaviours compared with peak current controlled buck converter are observed in the valley current controlled buck converter. Analysis and simulation results are verified by experimental results.

https://iopscience.iop.org/article/10.1088/1674-1056/19/5/050509/pdf

Dynamical analysis and experimental verification of valley current controlled buck converter

In this paper, the low-frequency oscillation phenomenon in a pulse train (PT) controlled buck converter operating in continuous conduction mode (CCM) is found and studied. The mechanism of this low-frequency oscillation phenomenon and the way to suppress it are studied. The time-domain simulation results and their corresponding phase portraits indicate that the equivalent series resistance (ESR) of the output filter capacitor has a critical effect on this low-frequency oscillation phenomenon. When the ESR is zero or small enough, such a low-frequency oscillation phenomenon appears in the PT controlled CCM buck converter because the output voltage can not be regulated timely. With the increase of ESR, the PT controlled CCM buck converter operates chaotically. The output voltage can be regulated timely and such a low-frequency oscillation phenomenon can be suppressed effectively. Experimental results are provided to verify the theoretical analyses and the simulations.

Analysis of low-frequency oscillation phenomenon in the pulsetrain controlled buck converter

The discrete iterative map models of peak current-mode (PCM) and valley current-mode (VCM) controlled buck converters, boost converters, and buck–boost converters with ramp compensation are established and their dynamical behaviours are investigated by using the operation region, parameter space map, bifurcation diagram, and Lyapunov exponent spectrum. The research results indicate that ramp compensation extends the stable operation range of the PCM controlled switching dc-dc converter to D > 0.5 and that of the VCM controlled switching dc–dc converter to D < 0.5. Compared with PCM controlled switching dc–dc converters with ramp compensation, VCM controlled switching dc–dc converters with ramp compensation exhibit interesting symmetrical dynamics. Experimental results are given to verify the analysis results in this paper.

https://iopscience.iop.org/article/10.1088/1674-1056/19/6/060508/pdf

Zhou Guo-Hua

Papers

Chaotic memristive circuit: equivalent circuit realization and dynamical analysis

Study of the Game Model of E-Commerce Information Sharing in an Agricultural Product Supply Chain based on fuzzy big data and LSGDM

Dynamical analysis and experimental verification of valley current controlled buck converter

Analysis of low-frequency oscillation phenomenon in the pulsetrain controlled buck converter

Symmetrical dynamics of peak current-mode and valley current-mode controlled switching dc-dc converters with ramp compensation