Chaos control using small-amplitude damping signals of the extended Duffing equation

Lazzouni, Sihem; Bowong, Samuel; Kakmeni, F. M. Moukam; Cherki, Brahim; Ghouali, Noureddine

doi:10.1016/j.cnsns.2005.08.004

Cited by 19 publications

(3 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The parameter values r 1 = 0.05, r 2 = −1, r 3 = 1, r 4 = 0.8, r 5 = 1.5, and ω = 1 are chosen, respectively, in the simulation to ensure the existence of chaos as shown in Fig. 4 [31]. Initial conditions were arbitrarily located at the origin.…”

Section: Adaptive Synchronization Of Two Strictly Different Systemsmentioning

confidence: 99%

Adaptive synchronization of chaotic systems with unknown bounded uncertainties via backstepping approach

Bowong

2007

Nonlinear Dyn

Self Cite

View full text Add to dashboard Cite

Backstepping design is proposed for adaptive synchronization of a class of chaotic systems with unknown bounded uncertainties. An adaptive backstepping control law is derived to make the error signals between the master and slave systems asymptotically synchronized without knowing the upper-bounds of the uncertainties in advance. The stability analysis is proved by using a well-known Lyapunov stability. Two illustrative examples are presented to show the effectiveness of the proposed adaptive chaos synchronization.

show abstract

Section: Adaptive Synchronization Of Two Strictly Different Systemsmentioning

confidence: 99%

Adaptive synchronization of chaotic systems with unknown bounded uncertainties via backstepping approach

Bowong

2007

Nonlinear Dyn

Self Cite

View full text Add to dashboard Cite

show abstract

“…In addition, many other systems with external perturbations have been widely investigated by using analytic methods and numerical simulations. [22][23][24][25] However, there are few studies of external perturbation for fiber-optic signal models. In fact, the fiber-optic signal propagation will be affected by lots of interference in the process of real propagation.…”

Section: Introductionmentioning

confidence: 99%

Chaos control in the nonlinear Schrödinger equation with Kerr law nonlinearity

Yin¹,

Zhao²,

Li-xin³

2014

Chinese Phys. B

View full text Add to dashboard Cite

The nonlinear Schrödinger equation with Kerr law nonlinearity in the two-frequency interference is studied by the numerical method. Chaos occurs easily due to the absence of damping. This phenomenon will cause the distortion in the process of information transmission. We find that fiber-optic transmit signals still present chaotic phenomena if the control intensity is smaller. With the increase of intensity, the fiber-optic signal can stay in a stable state in some regions. When the strength is suppressed to a certain value, an unstable phenomenon of the fiber-optic signal occurs. Moreover we discuss the sensitivities of the parameters to be controlled. The results show that the linear term coefficient and the environment of two quite different frequences have less effects on the fiber-optic transmission. Meanwhile the phenomena of vibration, attenuation and escape occur in some regions.

show abstract

“…In 1990, Ott et al [14] showed that a chaotic attractor could be converted to any one of a large number of possible attracting time-periodic motions by making only small time-dependent parameter perturbation. This method is called OGY method and it is a kind of feedback control [14][15][16][17]. Feedback control methods are used to control chaos by stabilizing a desired unstable periodic solution which is embedded in chaotic attractors.…”

Section: Introductionmentioning

confidence: 99%

Chaos suppression of a subsonic panel with geometric nonlinearity based on Melnikov’s method

Tang

Yang

2013

Int. J. Dynam. Control

View full text Add to dashboard Cite

Melnikov's method was adopted to study chaotic vibrations and chaos suppression of a two-dimensional subsonic panel with geometric nonlinearity subjected to external excitation. A Galerkin-type solution was introduced to derive the aerodynamic pressure from the linearized potential equation. Galerkin method was used to transform the governing partial differential equation to a series of ordinary differential equations. Based on Melnikov's method, the chaotic behaviors of the panel system were analyzed and suppressed by adding a parametric excitation term to the chaotic system. The numerical results illustrating the feasibility of the method are presented as bifurcation diagrams, phase plots, Poincaré maps, time-history diagrams and maximum Lyapunov exponent diagrams. The method used in this paper leads to fully consistent results. Comparison between the first-order and four-order expansion shows that the first-order expansion can qualitatively reflect the dynamical features of the plate.

show abstract

Chaos control using small-amplitude damping signals of the extended Duffing equation

Cited by 19 publications

References 31 publications

Adaptive synchronization of chaotic systems with unknown bounded uncertainties via backstepping approach

Adaptive synchronization of chaotic systems with unknown bounded uncertainties via backstepping approach

Chaos control in the nonlinear Schrödinger equation with Kerr law nonlinearity

Chaos suppression of a subsonic panel with geometric nonlinearity based on Melnikov’s method

Contact Info

Product

Resources

About