Dynamical analysis of a new chaotic system: asymmetric multistability, offset boosting control and circuit realization

In the chaos literature, there is currently significant interest in the discovery of new chaotic systems with hidden chaotic attractors. A new 4-D chaotic system with only two quadratic nonlinearities is investigated in this work. First, we derive a no-equilibrium chaotic system and show that the new chaotic system exhibits hidden attractor. Properties of the new chaotic system are analyzed by means of phase portraits, Lyapunov chaos exponents, and Kaplan-Yorke dimension. Then an electronic circuit realization is shown to validate the chaotic behavior of the new 4-D chaotic system. Finally, the physical circuit experimental results of the 4-D chaotic system show agreement with numerical simulations.

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Dynamical analysis of a new multistable chaotic system with hidden attractor: Antimonotonicity, coexisting multiple attractors, and offset boosting

Physics Letters A ◽

10.1016/j.physleta.2019.02.005 ◽

2019 ◽

Vol 383 (13) ◽

pp. 1450-1456 ◽

Cited By ~ 35

Author(s):

Atiyeh Bayani ◽

Karthikeyan Rajagopal ◽

Abdul Jalil M. Khalaf ◽

Sajad Jafari ◽

G.D. Leutcho ◽

...

Keyword(s):

Chaotic System ◽

Dynamical Analysis ◽

Hidden Attractor ◽

Multiple Attractors ◽

Offset Boosting

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Dynamical Analysis and Periodic Solution of a Chaotic System with Coexisting Attractors

Complexity ◽

10.1155/2021/9948488 ◽

2021 ◽

Vol 2021 ◽

pp. 1-15

Author(s):

Mingshu Chen ◽

Zhen Wang ◽

Xiaojuan Zhang ◽

Huaigu Tian

Keyword(s):

Chaotic System ◽

Vector Fields ◽

Dynamical Analysis ◽

Stable Node ◽

Polynomial Vector Fields ◽

Coexisting Attractors ◽

Poincaré Compactification ◽

Unstable Node ◽

New Chaotic System ◽

Multiple Coexisting Attractors

Chaotic attractors with no equilibria, with an unstable node, and with stable node-focus are presented in this paper. The conservative solutions are investigated by the semianalytical and seminumerical method. Furthermore, multiple coexisting attractors are investigated, and circuit is carried out. To study the system’s global structure, dynamics at infinity for this new chaotic system are studied using Poincaré compactification of polynomial vector fields in R 3 . Meanwhile, the dynamics near the infinity of the singularities are obtained by reducing the system’s dimensions on a Poincaré ball. The averaging theory analyzes the periodic solution’s stability or instability that bifurcates from Hopf-zero bifurcation.

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A New Chaotic System with Multiple Attractors: Dynamic Analysis, Circuit Realization and S-Box Design

Entropy ◽

10.3390/e20010012 ◽

2017 ◽

Vol 20 (1) ◽

pp. 12 ◽

Cited By ~ 47

Author(s):

Qiang Lai ◽

Akif Akgul ◽

Chunbiao Li ◽

Guanghui Xu ◽

Ünal Çavuşoğlu

Keyword(s):

Dynamic Analysis ◽

Chaotic System ◽

Multiple Attractors ◽

Circuit Realization ◽

New Chaotic System

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A New 4D Chaotic System with Coexisting Hidden Chaotic Attractors

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127420501424 ◽

2020 ◽

Vol 30 (10) ◽

pp. 2050142

Author(s):

Lihua Gong ◽

Rouqing Wu ◽

Nanrun Zhou

Keyword(s):

Chaotic System ◽

Dynamic Characteristics ◽

Dynamic Properties ◽

Random Number Generator ◽

Phase Portraits ◽

Hidden Attractors ◽

System A ◽

Offset Boosting ◽

New Chaotic System ◽

Linear State

A new 4D chaotic system with infinitely many equilibria is proposed using a linear state feedback controller in the Sprott C system. Although the new 4D chaotic system has only two nonlinear terms, it has rich dynamic characteristics, such as hidden attractors and coexisting attractors. Besides, the freedom of offset boosting of a variable is achieved by adjusting a controlled constant. The dynamic characteristics of the new chaotic system are fully analyzed from the aspects of phase portraits, bifurcation diagrams, Lyapunov exponents and Poincaré maps. The corresponding analogue electronic circuit is designed and implemented to verify the new 4D chaotic system. By taking advantage of the complex dynamic properties of the new chaotic system, a random number generator algorithm is proposed.

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