Two-memristor-based chaotic system and its extreme multistability reconstitution via dimensionality reduction analysis

2019 ◽  
Vol 127 ◽  
pp. 354-363 ◽  
Author(s):  
Yunzhen Zhang ◽  
Zhong Liu ◽  
Huagan Wu ◽  
Shengyao Chen ◽  
Bocheng Bao
Keyword(s):  
Dimensionality Reduction ◽  
Chaotic System ◽  
Extreme Multistability

scholarly journals Composite One- to Six-Scroll Hidden Attractors in a Memristor-Based Chaotic System and Their Circuit Implementation

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Ying Li ◽  
Xiaozhu Xia ◽  
Yicheng Zeng ◽  
Qinghui Hong
Keyword(s):  
Fixed Point ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Circuit Implementation ◽  
Hidden Attractors ◽  
Coexisting Attractors ◽  
Extreme Multistability ◽  
Different Types ◽  
Hardware Circuit ◽  
New System

Chaotic systems with hidden multiscroll attractors have received much attention in recent years. However, most parts of hidden multiscroll attractors previously reported were repeated by the same type of attractor, and the composite of different types of attractors appeared rarely. In this paper, a memristor-based chaotic system, which can generate composite attractors with one up to six scrolls, is proposed. These composite attractors have different forms, similar to the Chua’s double scroll and jerk double scroll. Through theoretical analysis, we find that the new system has no fixed point; that is to say, all of the composite multiscroll attractors are hidden attractors. Additionally, some complicated dynamic behaviors including various hidden coexisting attractors, extreme multistability, and transient transition are explored. Moreover, hardware circuit using discrete components is implemented, and its experimental results supported the numerical simulations results.

scholarly journals Extreme multistability analysis of memristor-based chaotic system and its application in image decryption

AIP Advances ◽  
2017 ◽  
Vol 7 (12) ◽  
pp. 125204 ◽  
Author(s):  
Chuang Li ◽  
Fuhong Min ◽  
Qiusen Jin ◽  
Hanyuan Ma
Keyword(s):  
Chaotic System ◽  
Extreme Multistability

scholarly journals Dimensionality Reduction Reconstitution for Extreme Multistability in Memristor-Based Colpitts System

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Yunzhen Zhang ◽  
Zhong Liu ◽  
Mo Chen ◽  
Huagan Wu ◽  
Shengyao Chen ◽  
...  
Keyword(s):  
Dimensionality Reduction ◽  
Three Dimensional ◽  
Basins Of Attraction ◽  
Phase Portraits ◽  
Colpitts Oscillator ◽  
Dynamical Mechanism ◽  
Reduction Model ◽  
State Variable ◽  
Extreme Multistability ◽  
Variable Mapping

In this paper, a four-dimensional (4-D) memristor-based Colpitts system is reaped by employing an ideal memristor to substitute the exponential nonlinear term of original three-dimensional (3-D) Colpitts oscillator model, from which the initials-dependent extreme multistability is exhibited by phase portraits and local basins of attraction. To explore dynamical mechanism, an equivalent 3-D dimensionality reduction model is built using the state variable mapping (SVM) method, which allows the implicit initials of the 4-D memristor-based Colpitts system to be changed into the corresponding explicitly initials-related system parameters of the 3-D dimensionality reduction model. The initials-related equilibria of the 3-D dimensionality reduction model are derived and their initials-related stabilities are discussed, upon which the dynamical mechanism is quantitatively explored. Furthermore, the initials-dependent extreme multistability is depicted by two-parameter plots and the coexistence of infinitely many attractors is demonstrated by phase portraits, which is confirmed by PSIM circuit simulations based on a physical circuit.

Extreme Multistability and Antimonotonicity in a Shinriki Oscillator with Two Flux-Controlled Memristors

2021 ◽  
Vol 31 (11) ◽  
pp. 2150167
Author(s):  
Fuhong Min ◽  
Yizi Cheng ◽  
Lei Lu ◽  
Xinya Li
Keyword(s):  
Dimensionality Reduction ◽  
Deterministic Model ◽  
Dynamical Evolution ◽  
Constitutive Relationship ◽  
Analysis Model ◽  
Extreme Multistability ◽  
Before And After ◽  
Flux Charge ◽  
Relationship Of ◽  
Plane Equilibrium

This paper proposes a novel memristive chaotic circuit which originated from a Shinriki oscillator with two flux-controlled memristors of different polarities. This two-memristor-based Shinriki oscillator (TMSO) having a special plane equilibrium is prone to exhibiting the initial-dependent phenomenon of extreme multistability. To investigate its internal dynamics, a third-order dimensionality reduction model is established by utilizing the constitutive relationship of its memristor’s flux and charge. The uncertain plane equilibrium is transfered into some deterministic model that can accurately predict the dynamical evolution of the system, where interesting phenomena of asymmetric bifurcations, extreme multistability and antimonotonicity are detected and analyzed by evaluating the position and stability of the equilibria in the flux–charge model. The simulation is carried out via Multisim to validate the analysis model, and the comparison of the phase trajectories, before and after dimensionality reduction, shows that this oscillator is good for research and practical use.

Hidden extreme multistability generated from a novel memristive two-scroll chaotic system

2021 ◽  
pp. 147-164
Author(s):  
Victor Kamdoum Tamba ◽  
Francois Kapche Tagne ◽  
Arsene Loic Mbanda Biamou ◽  
Manuela Corazon Nkeing ◽  
Armand Nzeukou Takougang
Keyword(s):  
Chaotic System ◽  
Extreme Multistability ◽  
Hidden Extreme Multistability

Symmetric coexisting attractors and extreme multistability in chaotic system

2021 ◽  
pp. 2150458
Author(s):  
Xiaoxia Li ◽  
Chi Zheng ◽  
Xue Wang ◽  
Yingzi Cao ◽  
Guizhi Xu
Keyword(s):  
Chaotic System ◽  
Electronic Circuit ◽  
Phase Portraits ◽  
Hyperchaotic System ◽  
Coexisting Attractors ◽  
Extreme Multistability ◽  
New Chaotic System ◽  
Initial States ◽  
Parameter Ranges ◽  
New System

In this paper, a new four-dimensional (4D) chaotic system with two cubic nonlinear terms is proposed. The most striking feature is that the new system can exhibit completely symmetric coexisting bifurcation behaviors and four symmetric coexisting attractors with the same Lyapunov exponents in all parameter ranges of the system when taking different initial states. Interestingly, these symmetric coexisting attractors can be considered as unusual symmetrical rotational coexisting attractors, which is a very fascinating phenomenon. Furthermore, by using a memristor to replace the coupling resistor of the new system, an interesting 4D memristive hyperchaotic system with one unstable origin is constructed. Of particular surprise is that it can exhibit four groups of extreme multistability phenomenon of infinitely many coexisting attractors of symmetric distribution about the origin. By using phase portraits, Lyapunov exponent spectra, and coexisting bifurcation diagrams, the dynamics of the two systems are fully analyzed and investigated. Finally, the electronic circuit model of the new system is designed for verifying the feasibility of the new chaotic system.

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