Homoclinic bifurcation and chaos in Duffing oscillator driven by an amplitude-modulated force

Ravichandran, V.; Chinnathambi, V.; Rajasekar, S.

doi:10.1016/j.physa.2006.11.003

Cited by 31 publications

(15 citation statements)

References 22 publications

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“…Similarly, a periodic attractor might become unstable and be replaced by a chaotic attractor. Therefore, bifurcations of duffing equation can be seen as useful information for the detection of weak signal [18].…”

Section: Evaluation Indexes Of Duffing Oscillatormentioning

confidence: 99%

Fault Diagnosis of Broken Rotor Bars in Squirrel-Cage Induction Motor of Hoister Based on Duffing Oscillator and Multifractal Dimension

Zhao

Wang

Zhang

2014

Advances in Mechanical Engineering

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This paper is to propose a novel fault diagnosis method for broken rotor bars in squirrel-cage induction motor of hoister, which is based on duffing oscillator and multifractal dimension. Firstly, based on the analysis of the structure and performance of modified duffing oscillator, the end of transitional slope from chaotic area to large-scale cycle area is selected as the optimal critical threshold of duffing oscillator by bifurcation diagrams and Lyapunov exponent. Secondly, the phase transformation duffing oscillator from chaos to intermittent chaos is sensitive to the signals, whose frequency difference is quite weak from the reference signal. The spectrums of the largest Lyapunov exponents and bifurcation diagrams of the duffing oscillator are utilized to analyze the variance in different parameters of frequency. Finally, this paper is to analyze the characteristics of both single fractal (box-counting dimension) and multifractal and make a comparison between them. Multifractal detrended fluctuation analysis is applied to detect extra frequency component of current signal. Experimental results reveal that the method is effective for early detection of broken rotor bars in squirrel-cage induction motor of hoister.

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Section: Evaluation Indexes Of Duffing Oscillatormentioning

confidence: 99%

Fault Diagnosis of Broken Rotor Bars in Squirrel-Cage Induction Motor of Hoister Based on Duffing Oscillator and Multifractal Dimension

Zhao

Wang

Zhang

2014

Advances in Mechanical Engineering

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“…Recently, chaotic motions of many systems, for example, 6 -Rayleigh oscillator [18], Duffing oscillator [19], Gylden's problem [20], and nonsmooth systems [21], have been investigated by the Melnikov method. In this section, we use the Melnikov method to investigate the chaotic motions of system (4).…”

Section: Chaotic Motions Of the Systemmentioning

confidence: 99%

Chaotic Motions of the Duffing-Van der Pol Oscillator with External and Parametric Excitations

Zhou

Chen

2014

Shock and Vibration

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The chaotic motions of the Duffing-Van der Pol oscillator with external and parametric excitations are investigated both analytically and numerically in this paper. The critical curves separating the chaotic and nonchaotic regions are obtained. The chaotic feature on the system parameters is discussed in detail. Some new dynamical phenomena including the controllable frequency are presented for this system. Numerical results are given, which verify the analytical ones.

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“…Differentiating V along the trajectories of (6), we obtain () T V e Pe ePe  (9) Suppose that we are able to find a controller u such that Eq. Hence, the GPS error dynamics (6) is globally exponentially stable for all initial conditions (0) n e  R by Lyapunov stability theory [46].…”

Section: Ieee -31661mentioning

confidence: 99%

“…Recently, several applications for chaotic systems have been found like lasers [7][8], oscillators [9][10],ecology [11], cryptography [12][13][14], communications [15][16][17], data encryption [18], chemical reactions [19][20], etc.…”

Section: Introductionmentioning

confidence: 99%

Active controller design for the GPS of four-wing chaotic systems

Vaidyanathan

Pakiriswamy

2013

2013 Fourth International Conference on Computing, Communications and Networking Technologies (ICCCNT)

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Generalized projective synchronization (GPS) of chaotic systems is a new type of synchronization, which is a general form of synchronization compared to other types of synchronization such as complete synchronization (CS), antisynchronization (AS), hybrid synchronization (HS), projective synchronization (PS), etc. There are many types of techniques available for synchronizing chaotic systems such as delayed feedback control, sampled-data feedback control, sliding mode control, backstepping control, etc. In this paper, we have used active control method for GPS of four-wing chaotic systems, viz. Wang four-wing chaotic system (2009) and Liu four-wing chaotic system (2009). Explicitly, we derive active controllers for GPS of identical Wang four-wing chaotic systems, identical Liu fourwing chaotic systems and non-identical Wang and Liu four-wing chaotic systems. Main GPS results in this work have been proved with the help of Lyapunov stability theory. MATLAB plots are shown to demonstrate the GPS results for Wang and Liu fourwing chaotic systems.

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Homoclinic bifurcation and chaos in Duffing oscillator driven by an amplitude-modulated force

Cited by 31 publications

References 22 publications

Fault Diagnosis of Broken Rotor Bars in Squirrel-Cage Induction Motor of Hoister Based on Duffing Oscillator and Multifractal Dimension

Fault Diagnosis of Broken Rotor Bars in Squirrel-Cage Induction Motor of Hoister Based on Duffing Oscillator and Multifractal Dimension

Chaotic Motions of the Duffing-Van der Pol Oscillator with External and Parametric Excitations

Active controller design for the GPS of four-wing chaotic systems

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