Dynamics, synchronization and circuit implementation of a simple fractional-order chaotic system with hidden attractors

2020 ◽  
Vol 130 ◽  
pp. 109406 ◽  
Author(s):  
Mengjiao Wang ◽  
Xiaohan Liao ◽  
Yong Deng ◽  
Zhijun Li ◽  
Yongxin Su ◽  
...  
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Circuit Implementation ◽  
Hidden Attractors

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 A New Fractional-Order Chaotic System with Different Families of Hidden and Self-Excited Attractors

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 564 ◽  
Author(s):  
Jesus Munoz-Pacheco ◽  
Ernesto Zambrano-Serrano ◽  
Christos Volos ◽  
Sajad Jafari ◽  
Jacques Kengne ◽  
...  
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Chaotic Attractor ◽  
Equilibrium Points ◽  
Fractional Order System ◽  
Order System ◽  
Chaotic Attractors ◽  
Equilibrium System ◽  
Hidden Attractors ◽  
Hidden Chaotic Attractor

In this work, a new fractional-order chaotic system with a single parameter and four nonlinearities is introduced. One striking feature is that by varying the system parameter, the fractional-order system generates several complex dynamics: self-excited attractors, hidden attractors, and the coexistence of hidden attractors. In the family of self-excited chaotic attractors, the system has four spiral-saddle-type equilibrium points, or two nonhyperbolic equilibria. Besides, for a certain value of the parameter, a fractional-order no-equilibrium system is obtained. This no-equilibrium system presents a hidden chaotic attractor with a `hurricane’-like shape in the phase space. Multistability is also observed, since a hidden chaotic attractor coexists with a periodic one. The chaos generation in the new fractional-order system is demonstrated by the Lyapunov exponents method and equilibrium stability. Moreover, the complexity of the self-excited and hidden chaotic attractors is analyzed by computing their spectral entropy and Brownian-like motions. Finally, a pseudo-random number generator is designed using the hidden dynamics.

Bursting, Dynamics, and Circuit Implementation of a New Fractional-Order Chaotic System With Coexisting Hidden Attractors

2019 ◽  
Vol 14 (7) ◽  
Author(s):  
Meng Jiao Wang ◽  
Xiao Han Liao ◽  
Yong Deng ◽  
Zhi Jun Li ◽  
Yi Ceng Zeng ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Fractional Order ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Equilibrium Points ◽  
Neuroendocrine Cells ◽  
Order System ◽  
Hidden Attractors ◽  
Main Mode ◽  
Circuit Realization

Systems with hidden attractors have been the hot research topic of recent years because of their striking features. Fractional-order systems with hidden attractors are newly introduced and barely investigated. In this paper, a new 4D fractional-order chaotic system with hidden attractors is proposed. The abundant and complex hidden dynamical behaviors are studied by nonlinear theory, numerical simulation, and circuit realization. As the main mode of electrical behavior in many neuroendocrine cells, bursting oscillations (BOs) exist in this system. This complicated phenomenon is seldom found in the chaotic systems, especially in the fractional-order chaotic systems without equilibrium points. With the view of practical application, the spectral entropy (SE) algorithm is chosen to estimate the complexity of this fractional-order system for selecting more appropriate parameters. Interestingly, there is a state variable correlated with offset boosting that can adjust the amplitude of the variable conveniently. In addition, the circuit of this fractional-order chaotic system is designed and verified by analog as well as hardware circuit. All the results are very consistent with those of numerical simulation.

Analysis and Circuit Implementation of Fractional Order Multi-wing Hidden Attractors

2020 ◽  
Vol 138 ◽  
pp. 109894 ◽  
Author(s):  
Li Cui ◽  
Ming Lu ◽  
Qingli Ou ◽  
Hao Duan ◽  
Wenhui Luo
Keyword(s):  
Fractional Order ◽  
Circuit Implementation ◽  
Hidden Attractors
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