Secure chaotic communication based on extreme multistability

Pisarchik, Alexander N.; Jaimes-Reátegui, R.; Rodríguez-Flores, C; García-López, J. H.; Huerta-Cuéllar, G.; Martín-Pasquín, Francisco Javier

doi:10.1016/j.jfranklin.2021.01.013

Cited by 54 publications

(13 citation statements)

References 19 publications

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“…Multistability is an exciting feature of dynamical systems [24][25][26]. Multistable oscillators have various applications [27]. A multistable oscillator with various attractors was discussed in [28].…”

Section: Introductionmentioning

confidence: 99%

A Chaotic Quadratic Oscillator with Only Squared Terms: Multistability, Impulsive Control, and Circuit Design

Dhinakaran¹,

Alanezi

Natiq³

et al. 2022

Symmetry

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Here, a chaotic quadratic oscillator with only squared terms is proposed, which shows various dynamics. The oscillator has eight equilibrium points, and none of them is stable. Various bifurcation diagrams of the oscillator are investigated, and its Lyapunov exponents (LEs) are discussed. The multistability of the oscillator is discussed by plotting bifurcation diagrams with various initiation methods. The basin of attraction of the oscillator is discussed in two planes. Impulsive control is applied to the oscillator to control its chaotic dynamics. Additionally, the circuit is implemented to reveal its feasibility.

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Section: Introductionmentioning

confidence: 99%

A Chaotic Quadratic Oscillator with Only Squared Terms: Multistability, Impulsive Control, and Circuit Design

Dhinakaran¹,

Alanezi

Natiq³

et al. 2022

Symmetry

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“…e attractors of multistable systems can have chaotic or hyperchaotic behaviors [24], as well as some other features such as having a number of scrolls [25]. Multistable systems can have some applications such as secure communication [26]. Multistability is also investigated in natural phenomena such as the brain [27].…”

Section: Introductionmentioning

confidence: 99%

A New Megastable Chaotic Oscillator with Blinking Oscillation terms

Dhinakaran¹,

Natiq²,

Al-Saidi

et al. 2021

Complexity

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Recently, megastable systems have grabbed many researchers’ interests in the area of nonlinear dynamics and chaotic systems. In this paper, the oscillatory terms’ coefficients of the simplest megastable oscillator are forced to blink in time. The forced system can generate an infinitive number of hidden attractors without changing parameters. The behavior of these hidden attractors can be chaotic, tori, and limit cycle. The attractors’ topology of the system seems unique and looks like picture frames. Besides, the existence of different coexisting attractors with different kinds of behaviors reflects the system's high sensitivity. Using the sample entropy algorithm, the system’s complexity for different initial values is assessed. In addition, the circuit of the introduced forced system is designed, and the possibility of implicating the system with analog elements is investigated.

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“…However, for instance, the hidden attractor can be generated by a system without equilibria [3][4][5] or with one stable zero equilibrium [6][7][8]. Meanwhile, there is a concept in the nonlinear systems, which is the "extreme multistability" [9][10][11][12]. Those attractors are obtained in a multistability system with given parameters but using different initial conditions.…”

Section: Introductionmentioning

confidence: 99%

Localization of Hidden Attractors in Chua’s System With Absolute Nonlinearity and Its FPGA Implementation

Wang

2021

Front. Phys.

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Investigation of the classical self-excited and hidden attractors in the modified Chua’s circuit is a hot and interesting topic. In this article, a novel Chua’s circuit system with an absolute item is investigated. According to the mathematical model, dynamic characteristics are analyzed, including symmetry, equilibrium stability analysis, Hopf bifurcation analysis, Lyapunov exponents, bifurcation diagram, and the basin of attraction. The hidden attractors are located theoretically. Then, the coexistence of the hidden limit cycle and self-excited chaotic attractors are observed numerically and experimentally. The numerical simulation results are consistent with the FPGA implementation results. It shows that the hidden attractor can be localized in the digital circuit.

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Secure chaotic communication based on extreme multistability

Cited by 54 publications

References 19 publications

A Chaotic Quadratic Oscillator with Only Squared Terms: Multistability, Impulsive Control, and Circuit Design

A Chaotic Quadratic Oscillator with Only Squared Terms: Multistability, Impulsive Control, and Circuit Design

A New Megastable Chaotic Oscillator with Blinking Oscillation terms

Localization of Hidden Attractors in Chua’s System With Absolute Nonlinearity and Its FPGA Implementation

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