Extreme Multistability in a Hyperjerk Memristive System With Hidden Attractors

Prousalis, Dimitrios A.; Volos, Christos; Bao, Bocheng; Meletlidou, E.; Stouboulos, I. N.; Kyprianidis, I. Μ.

doi:10.1016/b978-0-12-815838-8.00006-6

Cited by 12 publications

(5 citation statements)

References 39 publications

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“…Oscillators with time delays in their equations [13], fractional equations [14], fuzzy differential equations [15], those with hyperchaos [16], and others with synchronization among a group of them [17] can be examples of chaotic systems with specific features. Multistability is another of these features [18]. A system can be named multistable when it has more than one attractor without any change in its parameters [19].…”

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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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 there has been growing attention in finding chaotic systems with special qualities. Systems with no equilibrium [3], [4], with stable equilibria [5], [6], with curves of equilibria [7][8][9], with surface of equilibria [10][11][12], with multi-scroll attractors [13], with hidden attractors [14], [15], with amplitude control [16], [17], with simplest form , having hyperchaos [18][19][20], having fractional order form [21][22][23], with topological horseshoes [24], [25], and with extreme multistability [26][27][28][29], are examples of them. Another major category of chaotic systems includes periodically-forced nonlinear oscillators [30].…”

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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“…Some Scientists teams focus their works on this particular field. This include Kengne team [5,6,[8][9][10][11], B. Bao team [12][13][14][15] just to name a few, because of their applications in various domains such as telecommunication, Engineering, and neural network [16].…”

Section: Introductionmentioning

confidence: 99%

“…The work proposes a novel 4D autonomous dynamics system with five line equilibria which experiences the extreme multistability phenomenon. It is important to mention that most of the dynamics system that experience the extreme multistability are flux-control memristor-based circuits nowadays [12][13][17][18][19][20]. Due to the fact that the memristor device presented by HP company in 2008 is not yet marketable, almost all the above-mentioned extreme multistability dynamic systems are achieved using a simulator or emulator of memristor component.…”

Section: Introductionmentioning

confidence: 99%

Uncertain Destination of a 4D Autonomous System with Five Line Equilibria

Tapche¹

2020

IJST

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Objectives: This paper introduces a novel 4D autonomous dynamic system with five line equilibria and a smooth nonlinearity. Methods/ statistical analysis: The new model is obtained by adding one more freedom degree to the 3D jerk system recently introduced by Kengne and Mogue, 2018. To analyze and study the model, Ruth criterion principle is used for the stability of different lines equilibria. Using traditional dynamics tools such as bifurcation diagrams, phase portraits, Poincare section, power spectrum, and Pspice software, the dynamic of the system is carried out. Findings: The new elegant system has an extremely rich dynamics predominated by the phenomenon of extreme multistability. The various sequences of coexisting route to chaos (coexisting bifurcation) confirm the uncertain destination of our novel elegant system. Note that, for the best of author's knowledge, this is one of the best reproducible extreme multistable system because is not a flux control memristorbased system. Application/improvements: The results obtained in this investigation enrich the literature and being used to improve the extreme multistability application in many research domains such as Random Number Generation (RNG) and image encryption.

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Extreme Multistability in a Hyperjerk Memristive System With Hidden Attractors

Cited by 12 publications

References 39 publications

A New Megastable Chaotic Oscillator with Blinking Oscillation terms

A New Megastable Chaotic Oscillator with Blinking Oscillation terms

A Novel Mega-stable Chaotic Circuit

Uncertain Destination of a 4D Autonomous System with Five Line Equilibria

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