Controlling extreme multistability of memristor emulator-based dynamical circuit in flux–charge domain

Chen, Mo; Sun, Mengxia; Bao, Bocheng; Wu, Huagan; Xu, Quan; Wang, Jiang

doi:10.1007/s11071-017-3952-9

Cited by 113 publications

(64 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In recent years, multistability [20][21][22][23][24][25] and extreme multistability [26][27][28][29][30][31][32] have become research hotspots in the field of chaotic systems. Multistability means that when the system parameters remain unchanged, the system can generate more than one attractor with different initial values.…”

Section: Introductionmentioning

confidence: 99%

Heterogeneous and Homogenous Multistabilities in a Novel 4D Memristor-Based Chaotic System with Discrete Bifurcation Diagrams

et al. 2020

View full text Add to dashboard Cite

In this paper, a new 4D memristor-based chaotic system is constructed by using a smooth flux-controlled memristor to replace a resistor in the realization circuit of a 3D chaotic system. Compared with general chaotic systems, the chaotic system can generate coexisting infinitely many attractors. The proposed chaotic system not only possesses heterogeneous multistability but also possesses homogenous multistability. When the parameters of system are fixed, the chaotic system only generates two kinds of chaotic attractors with different positions in a very large range of initial values. Different from other chaotic systems with continuous bifurcation diagrams, this system has discrete bifurcation diagrams when the initial values change. In addition, this paper reveals the relationship between the symmetry of coexisting attractors and the symmetry of initial values in the system. The dynamic behaviors of the new system are analyzed by equilibrium point and stability, bifurcation diagrams, Lyapunov exponents, and phase orbit diagrams. Finally, the chaotic attractors are captured through circuit simulation, which verifies numerical simulation.

show abstract

Section: Introductionmentioning

confidence: 99%

Heterogeneous and Homogenous Multistabilities in a Novel 4D Memristor-Based Chaotic System with Discrete Bifurcation Diagrams

et al. 2020

View full text Add to dashboard Cite

show abstract

“…There is a good expectation that memristors will find use in a wide range of applications. In addition, it is necessary to use off-the-shelf components, such as resistor (R), capacitor (C), inductor (L), operational amplifier, analog multiplier, and other components to design a variety of equivalent realization circuits for the memristor [34,35] until the memristor can be manufactured at a low cost. Itoh and Chua replaced the Chua's oscillator with a piece-wise linear function memristor, standardized the diode in the Chua's oscillator with a memristor [36], and thus obtained two types of memristor-based chaotic oscillation circuits for the first time.…”

Section: Introductionmentioning

confidence: 99%

A High Spectral Entropy (SE) Memristive Hidden Chaotic System with Multi-Type Quasi-Periodic and its Circuit

Liu

Liang

et al. 2019

Entropy

View full text Add to dashboard Cite

As a new type of nonlinear electronic component, a memristor can be used in a chaotic system to increase the complexity of the system. In this paper, a flux-controlled memristor is applied to an existing chaotic system, and a novel five-dimensional chaotic system with high complexity and hidden attractors is proposed. Analyzing the nonlinear characteristics of the system, we can find that the system has new chaotic attractors and many novel quasi-periodic limit cycles; the unique attractor structure of the Poincaré map also reflects the complexity and novelty of the hidden attractor for the system; the system has a very high complexity when measured through spectral entropy. In addition, under different initial conditions, the system exhibits the coexistence of chaotic attractors with different topologies, quasi-periodic limit cycles, and chaotic attractors. At the same time, an interesting transient chaos phenomenon, one kind of novel quasi-periodic, and weak chaotic hidden attractors are found. Finally, we realize the memristor model circuit and the proposed chaotic system use off-the-shelf electronic components. The experimental results of the circuit are consistent with the numerical simulation, which shows that the system is physically achievable and provides a new option for the application of memristive chaotic systems.

show abstract

“…8 The dynamical stability of these chaotic systems is described related to their initial conditions, which signifies that there are numerous attractors in the system. 9,10 Coupled systems can display a strange form of multistability, specifically, the coexistence of infinitely many attractors for a specified group of parameters. This extreme multi-stability is revealed to be found in coupled systems with diverse kinds of coupling.…”

Section: Introductionmentioning

confidence: 99%

Coexisting infinitely many attractors in a new chaotic system with a curve of equilibria: Its extreme multi-stability and Kolmogorov–Sinai entropy computation

Ahmadi

Wang

Nazarimehr

et al. 2019

Advances in Mechanical Engineering

View full text Add to dashboard Cite

A new five-dimensional chaotic system with extreme multi-stability is introduced in this article. The mathematical model is established, and numerical simulations are done. This dynamical system complicates incident of extreme multi-stability. Most significantly, relied on the mathematical model, the recently proposed system has a curve of equilibria that ends in the occurrence of hidden attractors. We examine the initial-condition-dependent dynamics of this system. We inspect that there is an unrestricted number of coexistent attractors, which signifies the occurrence of extreme multi-stability strictly. In addition, the extreme multi-stability according to initial condition is investigated consuming the Lyapunov exponent spectra and bifurcation diagrams. The existence of coexisting infinitely many attractors is displayed with phase portraits. In the end, we calculate and debate Kolmogorov–Sinai entropy in the chaotic system. We direct trying the Kolmogorov–Sinai technique of entropic inspection for the dynamics of the system.

show abstract

Controlling extreme multistability of memristor emulator-based dynamical circuit in flux–charge domain

Cited by 113 publications

References 41 publications

Heterogeneous and Homogenous Multistabilities in a Novel 4D Memristor-Based Chaotic System with Discrete Bifurcation Diagrams

Heterogeneous and Homogenous Multistabilities in a Novel 4D Memristor-Based Chaotic System with Discrete Bifurcation Diagrams

A High Spectral Entropy (SE) Memristive Hidden Chaotic System with Multi-Type Quasi-Periodic and its Circuit

Coexisting infinitely many attractors in a new chaotic system with a curve of equilibria: Its extreme multi-stability and Kolmogorov–Sinai entropy computation

Contact Info

Product

Resources

About