Chaos control in duffing system

Wang, Ruiqi; Deng, Jin; Jing, Zhujun

doi:10.1016/j.chaos.2005.03.038

Cited by 38 publications

(21 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Inspired by the research of the duffing system [11]- [13], we notice that chaos may occur easily in this system due to the absence of damping in system of Equation (1.2). This phenomenon will cause the distortion in the November 2014 | Volume 1 | e721 process of information transmission.…”

Section: Resultsmentioning

confidence: 99%

Analysis on the Propagation of the Fiber-Optic Signals in the Perturbed Nonlinear Schrodinger Equation

Xing¹,

Yin

Li³

2014

OALib

View full text Add to dashboard Cite

Chaos appears in the whole process of fiber-optic signal propagation with one external perturbation due to the absence of damping. Via adding a proper controller, chaos cannot be suppressed when the controller's strength is weak. With the increase of the controller strength, the fiber-optic signal can stay in a stable state. However, unstable phenomenon occurs in the propagation of the fiber-optic signal when the strength exceeds a certain degree. Moreover, we discuss the parameters' sensitivity to be controlled. Numerical results show that vibration, oscillation and escape can occur during the transmission of optic signals with different parametric regions.

show abstract

Section: Resultsmentioning

confidence: 99%

Analysis on the Propagation of the Fiber-Optic Signals in the Perturbed Nonlinear Schrodinger Equation

Xing¹,

Yin

Li³

2014

OALib

View full text Add to dashboard Cite

show abstract

“…It is perhaps influenced by external environmental perturbations. As we know, the addition of a perturbation to an equation may lead to chaotic dynamics [31][32][33][34][35]. A few researchers have focussed on the complex dynamics and chaotic behaviors of perturbed nonlinearly dispersive equations.…”

Section: Introductionmentioning

confidence: 99%

“…Inspired by the nonlinear Duffing system [31,34], the controller would be chosen with the following damping term.…”

Section: Introductionmentioning

confidence: 99%

Melnikov analysis and chaos control of nonlinear dispersive KdV equation under external periodic perturbation

Yin

Xing

2014

Indian J Phys

View full text Add to dashboard Cite

The behavior of non-smooth solitary waves switching to chaos is studied. Firstly, we present some singular homoclinic orbits of an unperturbed system. These singular homoclinic orbits correspond to non-smooth solutions. Secondly, we find that the peculiar solitary waves are more likely to be chaos by using the Melnikov theory. Finally, chaos thresholds under different amplitudes and frequencies of a periodic perturbation are given. One interesting finding is that there exists a peculiar perturbation frequency, which has significant effect on the system. The system is not well-controlled under this frequency. However, the system can be well controlled, when the frequency of the perturbation surpasses the peculiar perturbation frequency with fixed parameters of the unperturbed system.

show abstract

“…One of the famous masterpieces is a kind of feedback control OGY method [4], which uses some weak feedback control to make the chaotic trajectory approach and settle down finally to a desired stabilized periodic orbit, formerly unstably embedded in the chaotic manifold. The other one is a kind of non-feedback control, which usually uses given external or parametric excitations to control the behavior of a system [6][7]. Meanwhile due to the progress of computer and digital signal processing technology, the discrete-time model of chaotic systems can be easily obtained [8] and research in discrete-time control has become intensified in recent years [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

“…However, the chaos behavior in some engineering system is highly unexpected because it will influence performance of system. In recent years, growing interests from physics, chemistry, biology, and engineering have stimulated the studies of chaos control techniques [1][2][3][4][5][6]. Several control methods leading to suppression of chaos have been presented.…”

Section: Introductionmentioning

confidence: 99%

Robust Control Design for Discrete Chaotic Systems with Unmatched Uncertainties

Tsai

Fang

Yan

et al. 2016

Proceedings of the 4th IIAE International Conference on Intelligent Systems and Image Processing 2016

View full text Add to dashboard Cite

This paper is concerned with the robust control for a general class of discrete chaotic systems with unmatched uncertainties. It is implemented by using discrete sliding mode control (DSMC). The proposed DSMC ensures the existence of the sliding mode. The chaotic behavior can be inhibited in an estimated bound in the state space even with unmatched uncertainties, which is not well addressed in the literature. The numerical simulation results demonstrate the feasibility and effectiveness of the proposed scheme.

show abstract

Chaos control in duffing system

Cited by 38 publications

References 29 publications

Analysis on the Propagation of the Fiber-Optic Signals in the Perturbed Nonlinear Schrodinger Equation

Analysis on the Propagation of the Fiber-Optic Signals in the Perturbed Nonlinear Schrodinger Equation

Melnikov analysis and chaos control of nonlinear dispersive KdV equation under external periodic perturbation

Robust Control Design for Discrete Chaotic Systems with Unmatched Uncertainties

Contact Info

Product

Resources

About