Chaos control in the uncertain Duffing oscillator

Bowong, Samuel; Kakmeni, F. M. Moukam; Dimi, Jean Luc

doi:10.1016/j.jsv.2005.09.009

Cited by 13 publications

(10 citation statements)

References 23 publications

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“…The Duffing system and the Genesio-Tesi system have been investigated extensively in the literatures [10][11][12][13][14][15][16]. Compared with those special chaotic systems studied in [10][11][12][13][14][15][16], system (1) has more research values.…”

Section: Remarkmentioning

confidence: 99%

“…Compared with those special chaotic systems studied in [10][11][12][13][14][15][16], system (1) has more research values.…”

Section: Remarkmentioning

confidence: 99%

“…For the sake of stabilizing the trajectories of system (21) to its origin, we take the following function as the first Lyapunov candidate According to (14), we have…”

Section: The Control Of Four-dimensional Systemmentioning

confidence: 99%

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The robust adaptive control of chaotic systems with unknown parameters and external disturbance via a scalar input

Luo

2015

Adaptive Control & Signal

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This paper investigates the control of chaotic systems in the presence of unknown parameters, model uncertainties, and external disturbance. We first discuss the control of a class of chaotic systems and then investigate the control of general chaotic systems. Based on the adaptive control scheme, some novel criteria are proposed via a backstepping-like procedure. As an example, the control of the Zhang hyperchaotic system is investigated via a single input. Some numerical simulations are given to demonstrate the robustness and efficiency of the proposed approach.

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Section: Remarkmentioning

confidence: 99%

“…Compared with those special chaotic systems studied in [10][11][12][13][14][15][16], system (1) has more research values.…”

Section: Remarkmentioning

confidence: 99%

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The robust adaptive control of chaotic systems with unknown parameters and external disturbance via a scalar input

Luo

2015

Adaptive Control & Signal

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“…Pyragas in 1992 presented a delayed feedback strategy for chaos control [8,9]. In addition, Lyapunov based control [10], feedback linearization [11], sliding mode [12], fuzzy control [13,14], adaptive control [15], and many other methods have been widely used for stabilizing periodic orbits of chaotic systems. In this paper a nonlinear feedback strategy based on an input-output linearization technique is used for chaos control in the model of spinning disks single mode oscillations presented in [5].…”

Section: Introductionmentioning

confidence: 99%

Chaos control in lateral oscillations of spinning disks via nonlinear feedback

Salarieh

Sadeghian

Merat

2009

Nonlinear Analysis: Real World Applications

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“…Complex phenomena such as bifurcation and chaos have been widely observed in mechanical vibratory systems [1-3]. In recent years, nonlinear mechanisms of abnormal or disordered behaviors have also been suggested in biomedical systems [4-12].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamic mechanism of vocal tremor from voice analysis and model simulations

Jiang

2008

Journal of Sound and Vibration

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Nonlinear dynamic analysis and model simulations are used to study the nonlinear dynamic characteristics of vocal folds with vocal tremor, which can typically be characterized by low frequency modulation and aperiodicity. Tremor voices from patients with disorders such as paresis, Parkinson's disease, hyperfunction, and adductor spasmodic dysphonia show lowdimensional characteristics, differing from random noise. Correlation dimension analysis statistically distinguishes tremor voices from normal voices. Furthermore, a nonlinear tremor model is proposed to study the vibrations of the vocal folds with vocal tremor. Fractal dimensions and positive Lyapunov exponents demonstrate the evidence of chaos in the tremor model, where amplitude and frequency play important roles in governing vocal fold dynamics. Nonlinear dynamic voice analysis and vocal fold modeling may provide a useful set of tools for understanding the dynamic mechanism of vocal tremor in patients with laryngeal diseases.

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Chaos control in the uncertain Duffing oscillator

Cited by 13 publications

References 23 publications

The robust adaptive control of chaotic systems with unknown parameters and external disturbance via a scalar input

The robust adaptive control of chaotic systems with unknown parameters and external disturbance via a scalar input

Chaos control in lateral oscillations of spinning disks via nonlinear feedback

Nonlinear dynamic mechanism of vocal tremor from voice analysis and model simulations

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