Effects on the bifurcation and chaos in forced Duffing oscillator due to nonlinear damping

Sharma, Ankit; Patidar, Vinod; Purohit, G.; Sud, K. K.

doi:10.1016/j.cnsns.2011.10.032

Cited by 88 publications

(42 citation statements)

References 13 publications

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“…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%

“…In Section 2, we study the chaotic behavior of system of Equation (1.2) and the chaos can be controlled by finding an appropriate controller. In Section 3, we study the chaos control in controlled system by Melnikov method [11]- [15]. In Section 4, the bifurcation diagrams and the maximum Lyapunov exponents are given to support the theoretical analysis.…”

Section: Introductionmentioning

confidence: 99%

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

Xing¹,

Yin

Li³

2014

OALib

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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.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Xing¹,

Yin

Li³

2014

OALib

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“…Many scholars paid attention to the heteroclinic bifurcation and chaos phenomena of nonlinear Duffing oscillator [24][25][26]. For example, Yang and Sun et al [27,28] investigated the necessary condition for the generating chaos of a double-well Duffing oscillator with bounded noise excitations and time-delay feedback by Melnikov theory.…”

Section: Introductionmentioning

confidence: 99%

Heteroclinic Bifurcation Behaviors of a Duffing Oscillator with Delayed Feedback

Wen

Chen

Guo

2018

Shock and Vibration

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The heteroclinic bifurcation and chaos of a Duffing oscillator with forcing excitation under both delayed displacement feedback and delayed velocity feedback are studied by Melnikov method. The Melnikov function is analytically established to detect the necessary conditions for generating chaos. Through the analysis of the analytical necessary conditions, we find that the influences of the delayed displacement feedback and delayed velocity feedback are separable. Then the influences of the displacement and velocity feedback parameters on heteroclinic bifurcation and threshold value of chaotic motion are investigated individually. In order to verify the correctness of the analytical conditions, the Duffing oscillator is also investigated by numerical iterative method. The bifurcation curves and the largest Lyapunov exponents are provided and compared. From the analysis of the numerical simulation results, it could be found that two types of period-doubling bifurcations occur in the Duffing oscillator, so that there are two paths leading to the chaos in this oscillator. The typical dynamical responses, including time histories, phase portraits, and Poincare maps, are all carried out to verify the conclusions. The results reveal some new phenomena, which is useful to design or control this kind of system.

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“…Recently, Sharma et al (2012) have analysed the dynamical behaviour of forced Duffing oscillator under the presence of nonlinear damping term analytically as well as computationally. They have particularly observed the effect of nonlinear damping on the global dynamical behaviour of forced Duffing oscillator through Melnikov analysis, characterisation of parameter space through Lyapunov spectrum calculation, fractalness of basin boundaries and fractal dimensions etc.…”

Section: Introductionmentioning

confidence: 99%

“…Duffing oscillator describes the motion of a particle in double-well potential and it is represented by a ubiquitous nonlinear differential equation (Sharma et al, 2012). It has a number of applications not only in physical and engineering problems but also in biological problems.…”

Section: Introductionmentioning

confidence: 99%

An analogue circuit to study the forced and quadratically damped Duffing oscillator

Singh

Purohit

Sharma

et al. 2017

IJNDC

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Effects on the bifurcation and chaos in forced Duffing oscillator due to nonlinear damping

Cited by 88 publications

References 13 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

Heteroclinic Bifurcation Behaviors of a Duffing Oscillator with Delayed Feedback

An analogue circuit to study the forced and quadratically damped Duffing oscillator

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