Optimization of the Kaplan-Yorke dimension in fractional-order chaotic oscillators by metaheuristics

Silva-Juárez, Alejandro; Tlelo‐Cuautle, Esteban; Fraga, Luis Gerardo de la; Li, Rui

doi:10.1016/j.amc.2020.125831

Cited by 23 publications

(14 citation statements)

References 33 publications

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“…e first pioneering study was introduced by Pecora and Carrol in 1990 for chaos synchronization of the abovementioned model which has received a lot of attention from many areas such as encryption [17], FPGA implementation [18], optimization [19][20][21][22][23], electronic circuits [24], and Engineering [25].…”

Section: Introductionmentioning

confidence: 99%

[Retracted] A Novel of New 7D Hyperchaotic System with Self‐Excited Attractors and Its Hybrid Synchronization

Al-Obeidi¹,

Al-Azzawi

Hamad

et al. 2021

Computational Intelligence and Neuroscience

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In this study, a novel 7D hyperchaotic model is constructed from the 6D Lorenz model via the nonlinear feedback control technique. The proposed model has an only unstable origin point. Thus, it is categorized as a model with self-excited attractors. And it has seven equations which include 19 terms, four of which are quadratic nonlinearities. Various important features of the novel model are analyzed, including equilibria points, stability, and Lyapunov exponents. The numerical simulation shows that the new class exhibits dynamical behaviors such as chaotic and hyperchaotic. This paper also presents the hybrid synchronization for a novel model via Lyapunov stability theory.

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Section: Introductionmentioning

confidence: 99%

[Retracted] A Novel of New 7D Hyperchaotic System with Self‐Excited Attractors and Its Hybrid Synchronization

Al-Obeidi¹,

Al-Azzawi

Hamad

et al. 2021

Computational Intelligence and Neuroscience

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“…To improve the application of chaotic systems, optimization methods can be used [72]. ese single and multiobjective optimization methods have used different numerical approaches to increase (or decrease) the Lyapunov exponents [73], Kaplan-Yorke dimension [74], and complexity indexes [75]. Future works can focus on optimizing the indexes of the proposed system to provide its application in image encryption and random number generator.…”

Section: Discussionmentioning

confidence: 99%

Proposing and Dynamical Analysis of a Hyperjerk Piecewise Linear Chaotic System with Offset Boostable Variable and Hidden Attractors

Vijayakumar¹,

Jamal

Ali

et al. 2021

Complexity

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Designing chaotic systems with different properties helps to increase our knowledge about real-world chaotic systems. In this article, a piecewise linear (PWL) term is employed to modify a simple chaotic system and obtain a new chaotic model. The proposed model does not have any equilibrium for different values of the control parameters. Therefore, its attractor is hidden. It is shown that the PWL term causes an offset boostable variable. This feature provides more flexibility and controllability in the designed system. Numerical analyses show that periodic and chaotic attractors coexist in some fixed values of the parameters, indicating multistability. Also, the feasibility of the system is approved by designing field programmable gate arrays (FPGA).

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“…As the main search engine, CUDA-powered genetic algorithm was utilized. In contrast with paper [50], where individuals in population are in fact removed if carry parameter values that does not meet "chaotic assumptions", objective function receives serious penalization in the case of violation of conditions mentioned above. Detail calculation discovers several topologically different chaotic and hyperchaotic cases of mathematical model (2).…”

Section: Amplifier Chaotification Processmentioning

confidence: 97%

“…Interesting approach how to deal with a chaos localization problem is suggested in paper [50] where two-step procedure is suggested. Proposed optimization method can be marked as metaheuristic, combines differential evolution and particle swarm optimization.…”

Section: Amplifier Chaotification Processmentioning

confidence: 99%

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Hyperchaotic Self-Oscillations of Two-Stage Class C Amplifier With Generalized Transistors

Petržela

2021

IEEE Access

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This paper yields process of development, numerical analysis, lumped circuit modeling, and experimental verification of a new hyperchaotic oscillator based on the fundamental topology of two-stage amplifier. Analyzed network structure contains two generalized bipolar transistors connected with common emitter. Both transistors are initially modeled as two-ports via full admittance matrix, considering linear backward trans-conductance and polynomial forward trans-conductance. As proved in paper, these two scalar nonlinearities can push amplifier to exhibit robust hyperchaotic behavior with significantly high Kaplan-Yorke dimension. Regions of chaos and hyperchaos in a space of admittance parameters associated with both transistors are specified following the concept of positive values of Lyapunov exponents. Long time structural stability of generated hyperchaotic waveforms is proved by construction of flow-equivalent electronic circuit and experimental measurement, that is by screenshots captured by oscilloscope.INDEX TERMS Admittance parameters, bipolar transistor, class C amplifier, chaos, chaotic oscillator, hyperchaos, Lyapunov exponents, strange attractors.

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Optimization of the Kaplan-Yorke dimension in fractional-order chaotic oscillators by metaheuristics

Cited by 23 publications

References 33 publications

[Retracted] A Novel of New 7D Hyperchaotic System with Self‐Excited Attractors and Its Hybrid Synchronization

[Retracted] A Novel of New 7D Hyperchaotic System with Self‐Excited Attractors and Its Hybrid Synchronization

Proposing and Dynamical Analysis of a Hyperjerk Piecewise Linear Chaotic System with Offset Boostable Variable and Hidden Attractors

Hyperchaotic Self-Oscillations of Two-Stage Class C Amplifier With Generalized Transistors

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