Suppression of chaos in a generalized Duffing oscillator with fractional-order deflection

Du, Lin; Zhao, Yunping; Lei, Youming; Hu, Jian; Yue, Xiaole

doi:10.1007/s11071-018-4171-8

Cited by 18 publications

(12 citation statements)

References 38 publications

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“…Second, the area, A R , enclosed by the boundary function [Eq. (28)] is straightforwardly obtained from previous theory [7]: Observe that one finds A R ! 0 as δ !…”

Section: B Chaotic Threshold From Melnikov Analysismentioning

confidence: 99%

“…Furthermore, the use of Melnikov analysis (MA) techniques has allowed the development of a theoretical approach to chaos suppression in damped driven systems, and which involves adding periodic chaos-suppressing (CS) excitations [26]. This MAbased approach has been shown to be reliable in suppressing chaos in a Duffing oscillator by a fine choice of the shape of the external periodic excitation [27], a generalized Duffing oscillator with fractional-order deflection [28], coupled arrays of damped, periodically forced, nonlinear oscillators [29,30], as well as in starlike networks of dissipative nonlinear oscillators [31].…”

Section: Introductionmentioning

confidence: 99%

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Suppressing Chaos in Damped Driven Systems by Non-Harmonic Excitations: Experimental Robustness Against Potential's Mismatches

Palmero

Chacón

2022

Preprint

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The robustness of a chaos-suppressing scenario against potential mismatches is experimentally studied through the universal model of a damped, harmonically driven two-well Duffing oscillator subject to non-harmonic chaos-suppressing excitations. We consider a second order analogous electrical circuit having an extremely simple two-well potential that differs from that of the standard two-well Duffing model, and compare the main theoretical predictions regarding the chaos-suppressing scenario from the latter with experimental results from the former. Our experimental results prove the high robustness of the chaos-suppressing scenario against potential mismatches regardless of the (constant) values of the remaining parameters. Specifically, the predictions of an inverse dependence of the regularization area in the control parameter plane on the impulse of the chaos-suppressing excitation as well as of a minimal effective amplitude of the chaos-suppressing excitation when the impulse transmitted is maximum were experimentally confirmed.

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“…Second, the area, A R , enclosed by the boundary function [Eq. (28)] is straightforwardly obtained from previous theory [7]: Observe that one finds A R ! 0 as δ !…”

Section: B Chaotic Threshold From Melnikov Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Suppressing Chaos in Damped Driven Systems by Non-Harmonic Excitations: Experimental Robustness Against Potential's Mismatches

Palmero

Chacón

2022

Preprint

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“…19,20 However, they ignore that the essence of Duffing oscillator is a nonlinear elastic system, and the Duffing oscillator is analyzed from the perspective of mechanics. 21,22 Origin of Holmes-Duffing oscillator Generally, the restoring force of a one-dimensional elastic system is [23][24][25]…”

Section: Duffing Oscillator Study From the Perspective Of Mechanicsmentioning

confidence: 99%

Model modification and feature study of Duffing oscillator

Chen

Cao

De-zhi

2021

Journal of Low Frequency Noise, Vibration and Active Control

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With the development of chaos theory, Duffing oscillator has been extensively studied in many fields, especially in electronic signal processing. As a nonlinear oscillator, Duffing oscillator is more complicated in terms of equations or circuit analysis. In order to facilitate the analysis of its characteristics, the study analyzes the circuit from the perspective of vibrational science and energetics. The classic Holmes-Duffing model is first modified to make it more popular and concise, and then the model feasibility is confirmed by a series of rigorous derivations. According to experiments, the influence of driving force amplitude, frequency, and initial value on the system is finally explained by the basic theories of physics. Through this work, people can understand the mechanisms and characteristics of Duffing oscillator more intuitively and comprehensively. It provides a new idea for the study of Duffing oscillators and more.

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“…From tools that are used in the analysis of nonlinear systems, the most general tools are the frequency response curve 4 , 5 , 11 , 15 , 17 – 21 , 27 , 33 , 34 , 38 , the backbone curve 11 , 12 , 19 and, when the numerical approach is used, time histories 16 , 35 , 43 . In the group of more sophisticated tools, however, more specific techniques can also be mentioned: phase portraits 7 , 8 , 35 – 37 , bifurcation diagrams 8 , 38 , 39 , basins of attraction 40 and Poincaré maps 8 , 35 , 41 , 42 .…”

Section: Introductionmentioning

confidence: 99%

Duffing-type oscillator under harmonic excitation with a variable value of excitation amplitude and time-dependent external disturbances

Wawrzyński

2021

Sci Rep

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For more complex nonlinear systems, where the amplitude of excitation can vary in time or where time-dependent external disturbances appear, an analysis based on the frequency response curve may be insufficient. In this paper, a new tool to analyze nonlinear dynamical systems is proposed as an extension to the frequency response curve. A new tool can be defined as the chart of bistability areas and area of unstable solutions of the analyzed system. In the paper, this tool is discussed on the basis of the classic Duffing equation. The numerical approach was used, and two systems were tested. Both systems are softening, but the values of the coefficient of nonlinearity are significantly different. Relationships between both considered systems are presented, and problems of the nonlinearity coefficient and damping influence are discussed.

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Suppression of chaos in a generalized Duffing oscillator with fractional-order deflection

Cited by 18 publications

References 38 publications

Suppressing Chaos in Damped Driven Systems by Non-Harmonic Excitations: Experimental Robustness Against Potential's Mismatches

Suppressing Chaos in Damped Driven Systems by Non-Harmonic Excitations: Experimental Robustness Against Potential's Mismatches

Model modification and feature study of Duffing oscillator

Duffing-type oscillator under harmonic excitation with a variable value of excitation amplitude and time-dependent external disturbances

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