Constructing Infinitely Many Attractors in a Programmable Chaotic Circuit

Li, Chunbiao; Thio, Wesley; Sprott, Julien Clinton; Iu, Herbert Ho-Ching; Xu, Yujie

doi:10.1109/access.2018.2824984

Cited by 84 publications

(31 citation statements)

References 71 publications

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“…A new oscillator with infinite coexisting asymmetric attractors introduced in [31]. Some other such examples have been proposed recently [36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

A Novel Mega-stable Chaotic Circuit

Pham¹,

Ali²,

Al-Saidi³

et al. 2020

RADIOENGINEERING

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In recent years designing new multistable chaotic oscillators has been of noticeable interest. A multistable system is a double-edged sword which can have many benefits in some applications while in some other situations they can be even dangerous. In this paper, we introduce a new multistable two-dimensional oscillator. The forced version of this new oscillator can exhibit chaotic solutions which makes it much more exciting. Also, another scarce feature of this system is the complex basins of attraction for the infinite coexisting attractors. Some initial conditions can escape the whirlpools of nearby attractors and settle down in faraway destinations. The dynamical properties of this new system are investigated by the help of equilibria analysis, bifurcation diagram, Lyapunov exponents' spectrum, and the plot of basins of attraction. The feasibility of the proposed system is also verified through circuit implementation.

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“…A new oscillator with infinite coexisting asymmetric attractors introduced in [31]. Some other such examples have been proposed recently [36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

A Novel Mega-stable Chaotic Circuit

Pham¹,

Ali²,

Al-Saidi³

et al. 2020

RADIOENGINEERING

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“…Lai et al introduced some effective methods to construct chaotic systems with infinitely many coexisting strange attractors [23,24]. Li et al designed a programmable chaotic circuit with infinitely many chaotic attractors and established the coexistence of multiple attractors by simulation methods [25]. Bao et al found that memristor-based chaotic systems can generate different types of coexisting attractors [26,27].…”

Section: Introductionmentioning

confidence: 99%

Infinitely Many Coexisting Attractors in No-Equilibrium Chaotic System

et al. 2020

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is paper proposes a new no-equilibrium chaotic system that has the ability to yield infinitely many coexisting hidden attractors. Dynamic behaviors of the system with respect to the parameters and initial conditions are numerically studied. It shows that the system has chaotic, quasiperiodic, and periodic motions for different parameters and coexists with a large number of hidden attractors for different initial conditions. e circuit and microcontroller implementations of the system are given for illustrating its physical meaning. Also, the synchronization conditions of the system are established based on the adaptive control method.

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“…Many chaotic flows with various features are being proposed every year [ 14 , 15 , 16 ]. Researchers hope that such studies help to investigate the reason of generating chaotic attractors [ 17 , 18 , 19 , 20 ]. Dynamical properties of two discs with viscous friction and multiple delays have been studied in [ 21 ].…”

Section: Introductionmentioning

confidence: 99%

Entropy Analysis and Image Encryption Application Based on a New Chaotic System Crossing a Cylinder

Farhan

Al-Saidi

Maolood

et al. 2019

Entropy

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Designing chaotic systems with specific features is a hot topic in nonlinear dynamics. In this study, a novel chaotic system is presented with a unique feature of crossing inside and outside of a cylinder repeatedly. This new system is thoroughly analyzed by the help of the bifurcation diagram, Lyapunov exponents’ spectrum, and entropy measurement. Bifurcation analysis of the proposed system with two initiation methods reveals its multistability. As an engineering application, the system’s efficiency is tested in image encryption. The complexity of the chaotic attractor of the proposed system makes it a proper choice for encryption. States of the chaotic attractor are used to shuffle the rows and columns of the image, and then the shuffled image is XORed with the states of chaotic attractor. The unpredictability of the chaotic attractor makes the encryption method very safe. The performance of the encryption method is analyzed using the histogram, correlation coefficient, Shannon entropy, and encryption quality. The results show that the encryption method using the proposed chaotic system has reliable performance.

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Constructing Infinitely Many Attractors in a Programmable Chaotic Circuit

Cited by 84 publications

References 71 publications

A Novel Mega-stable Chaotic Circuit

A Novel Mega-stable Chaotic Circuit

Infinitely Many Coexisting Attractors in No-Equilibrium Chaotic System

Entropy Analysis and Image Encryption Application Based on a New Chaotic System Crossing a Cylinder

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