scholarly journals Generating hidden extreme multistability in memristive chaotic oscillator via micro‐perturbation

2018 ◽  
Vol 54 (13) ◽  
pp. 808-810 ◽  
Author(s):  
Lu Wang ◽  
Sen Zhang ◽  
Yi‐Cheng Zeng ◽  
Zhi‐Jun Li
Keyword(s):  
Chaotic Oscillator ◽  
Extreme Multistability ◽  
Hidden Extreme Multistability

Hidden Extreme Multistability, Antimonotonicity and Offset Boosting Control in a Novel Fractional-Order Hyperchaotic System Without Equilibrium

2018 ◽  
Vol 28 (13) ◽  
pp. 1850167 ◽  
Author(s):  
Sen Zhang ◽  
Yicheng Zeng ◽  
Zhijun Li ◽  
Chengyi Zhou
Keyword(s):  
Fractional Order ◽  
Initial Conditions ◽  
State Feedback Control ◽  
Hyperchaotic System ◽  
Hidden Attractors ◽  
System Parameters ◽  
Offset Boosting ◽  
Extreme Multistability ◽  
Hidden Extreme Multistability ◽  
New System

Recently, the notion of hidden extreme multistability and hidden attractors is very attractive in chaos theory and nonlinear dynamics. In this paper, by utilizing a simple state feedback control technique, a novel 4D fractional-order hyperchaotic system is introduced. Of particular interest is that this new system has no equilibrium, which indicates that its attractors are all hidden and thus Shil’nikov method cannot be applied to prove the existence of chaos for lacking hetero-clinic or homo-clinic orbits. Compared with other fractional-order chaotic or hyperchaotic systems, this new system possesses three unique and remarkable features: (i) The amazing and interesting phenomenon of the coexistence of infinitely many hidden attractors with respect to same system parameters and different initial conditions is observed, meaning that hidden extreme multistability arises. (ii) By varying the initial conditions and selecting appropriate system parameters, the striking phenomenon of antimonotonicity is first discovered, especially in such a fractional-order hyperchaotic system without equilibrium. (iii) An attractive special feature of the convenience of offset boosting control of the system is also revealed. The complex and rich hidden dynamic behaviors of this system are investigated by using conventional nonlinear analysis tools, including equilibrium stability, phase portraits, bifurcation diagram, Lyapunov exponents, spectral entropy complexity, and so on. Furthermore, a hardware electronic circuit is designed and implemented. The hardware experimental results and the numerical simulations of the same system on the Matlab platform are well consistent with each other, which demonstrates the feasibility of this new fractional-order hyperchaotic system.

scholarly journals Complex Dynamics in a Memcapacitor-Based Circuit

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 188 ◽  
Author(s):  
Fang Yuan ◽  
Yuxia Li ◽  
Guangyi Wang ◽  
Gang Dou ◽  
Guanrong Chen
Keyword(s):  
Complex System ◽  
Lyapunov Exponents ◽  
Dynamic Characteristics ◽  
Complex Dynamics ◽  
Basins Of Attraction ◽  
Chaotic Oscillator ◽  
Initial Condition ◽  
Circuit Implementation ◽  
Coexisting Attractors ◽  
Extreme Multistability

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 novel memristive 6D hyperchaotic autonomous system with hidden extreme multistability

2019 ◽  
Vol 120 ◽  
pp. 100-115 ◽  
Author(s):  
Brice Anicet Mezatio ◽  
Marceline Tingue Motchongom ◽  
Blaise Raoul Wafo Tekam ◽  
Romanic Kengne ◽  
Robert Tchitnga ◽  
...  
Keyword(s):  
Autonomous System ◽  
Extreme Multistability ◽  
Hidden Extreme Multistability

Hidden extreme multistability and its control with selection of a desired attractor in a non-autonomous Hopfield neuron

2021 ◽  
pp. 154059
Author(s):  
Isaac Sami Doubla ◽  
Balamurali Ramakrishnan ◽  
Zeric Tabekoueng Njitacke ◽  
Jacques Kengne ◽  
Kartikeyan Rajagopal
Keyword(s):  
Extreme Multistability ◽  
Hidden Extreme Multistability ◽  
Selection Of

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

Simplest Megastable Chaotic Oscillator

2019 ◽  
Vol 29 (13) ◽  
pp. 1950187 ◽  
Author(s):  
Sajad Jafari ◽  
Karthikeyan Rajagopal ◽  
Tasawar Hayat ◽  
Ahmed Alsaedi ◽  
Viet-Thanh Pham
Keyword(s):  
Nonlinear Dynamics ◽  
Bifurcation Diagram ◽  
Chaotic Systems ◽  
Basin Of Attraction ◽  
Chaotic Oscillator ◽  
Hidden Attractors ◽  
Coexisting Attractors ◽  
Extreme Multistability ◽  
Dynamical Properties ◽  
New System

Recently, chaotic systems with hidden attractors and multistability have been of great interest in the field of chaos and nonlinear dynamics. Two special categories of systems with multistability are systems with extreme multistability and systems with megastability. In this paper, the simplest (yet) megastable chaotic oscillator is designed and introduced. Dynamical properties of this new system are completely investigated through tools like bifurcation diagram, Lyapunov exponents, and basin of attraction. It is shown that between its countable infinite coexisting attractors, only one is self-excited and the rest are hidden.

scholarly journals Dynamic Analysis and Circuit Realization of a Novel No-Equilibrium 5D Memristive Hyperchaotic System with Hidden Extreme Multistability

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Qiuzhen Wan ◽  
Zhaoteng Zhou ◽  
Wenkui Ji ◽  
Chunhua Wang ◽  
Fei Yu
Keyword(s):  
Initial Conditions ◽  
Hyperchaotic System ◽  
Circuit Realization ◽  
System Parameters ◽  
Dynamical Characteristics ◽  
Offset Boosting ◽  
Extreme Multistability ◽  
Hidden Extreme Multistability ◽  
Dynamic Attractors ◽  
Lyapunov Exponent Spectrum

In this paper, a novel no-equilibrium 5D memristive hyperchaotic system is proposed, which is achieved by introducing an ideal flux-controlled memristor model and two constant terms into an improved 4D self-excited hyperchaotic system. The system parameters-dependent and memristor initial conditions-dependent dynamical characteristics of the proposed memristive hyperchaotic system are investigated in terms of phase portrait, Lyapunov exponent spectrum, bifurcation diagram, Poincaré map, and time series. Then, the hidden dynamic attractors such as periodic, quasiperiodic, chaotic, and hyperchaotic attractors are found under the variation of its system parameters. Meanwhile, the most striking phenomena of hidden extreme multistability, transient hyperchaotic behavior, and offset boosting control are revealed for appropriate sets of the memristor and other initial conditions. Finally, a hardware electronic circuit is designed, and the experimental results are well consistent with the numerical simulations, which demonstrate the feasibility of this novel 5D memristive hyperchaotic system.

Hidden extreme multistability in memristive hyperchaotic system

2017 ◽  
Vol 94 ◽  
pp. 102-111 ◽  
Author(s):  
B.C. Bao ◽  
H. Bao ◽  
N. Wang ◽  
M. Chen ◽  
Q. Xu
Keyword(s):  
Hyperchaotic System ◽  
Extreme Multistability ◽  
Hidden Extreme Multistability
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