Evaluating Lyapunov exponent spectra with neural networks

Maus, Adam; Sprott, Julien Clinton

doi:10.1016/j.chaos.2013.03.001

Cited by 35 publications

(18 citation statements)

References 18 publications

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“…Maus and Sprott 45 proposed a method to evaluate Lyapunov exponents using neural networks by constructing global models. This method aids in removing spurious positive Lyapunov exponents.…”

Section: B Neural Network Based Lyapunov Exponentmentioning

confidence: 99%

On the dynamics of ocean ambient noise: Two decades later

Siddagangaiah

Guo

et al. 2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Two decades ago, it was shown that ambient noise exhibits low dimensional chaotic behavior. Recent new techniques in nonlinear science can effectively detect the underlying dynamics in noisy time series. In this paper, the presence of low dimensional deterministic dynamics in ambient noise is investigated using diverse nonlinear techniques, including correlation dimension, Lyapunov exponent, nonlinear prediction, and entropy based methods. The consistent interpretation of different methods demonstrates that ambient noise can be best modeled as nonlinear stochastic dynamics, thus rejecting the hypothesis of low dimensional chaotic behavior. The ambient noise data utilized in this study are of duration 60 s measured at South China Sea.

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“…Maus and Sprott 45 proposed a method to evaluate Lyapunov exponents using neural networks by constructing global models. This method aids in removing spurious positive Lyapunov exponents.…”

Section: B Neural Network Based Lyapunov Exponentmentioning

confidence: 99%

On the dynamics of ocean ambient noise: Two decades later

Siddagangaiah

Guo

et al. 2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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show abstract

“…Accordingly, we can obtain 3 values of λ i = λ i (z − 0 , u i 0 ) by means of formulas (38) and (39) ranked from small to large as…”

Section: Mathematical Description Of the Spectrum Of Lyapunov Exponenmentioning

confidence: 99%

“…The good choice of such matrix is 0 = I. Then, we iterate the controlled hybrid Poincaré map (24) together with the linearization equation (39). For the kth iteration, the difference between two nearby orbits is then defined by the perturbation matrix…”

Section: Numerical Calculation Procedures Of the Spectrum Of Lyapunov mentioning

confidence: 99%

Computation of the Lyapunov exponents in the compass-gait model under OGY control via a hybrid Poincaré map

Gritli

Belghith

2015

Chaos, Solitons & Fractals

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“…Lyapunov exponents (LEs) are necessary and more convenient for detecting chaos in dynamical systems, and the existence of a positive Lyapunov exponent confirms the chaotic behavior of the system [8][9][10][11][12]. Time series based LEs calculation methods like Wolf algorithm [9], Jacobian method [10], and neural network algorithm [11] are popularly known ways of calculating Lyapunov exponents for integer and fractional order systems. To calculate the LEs of the HPS we use the Wolf method [9] and the total simulation time taken to calculate LEs is 20000s.…”

Section: Dynamic Analysis Of Hpsmentioning

confidence: 99%

Multistability in Horizontal Platform System with and without Time Delays

Rajagopal

Duraisamy

Weldegiorgis

2018

Shock and Vibration

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Chaotic behavior and bifurcation analysis of horizontal platform systems (HPS) have been investigated widely by many researchers. However, the multistable features of such systems have not been investigated, and hence we identified the multistable parameter and investigated the coexisting attractors of the HPS. To understand the effects of time delays on the nonautonomous and autonomous HPS, we introduced a constant time delay in the state feedback variable. Investigation of the bifurcation of the time delayed HPS with time delay and parameters reveals that the system behavior differs between the autonomous and nonautonomous HPS. To investigate the multistability existence in time delayed HPS, we plot the bifurcation of the autonomous HPS and show the multistability and coexisting attractors.

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Evaluating Lyapunov exponent spectra with neural networks

Cited by 35 publications

References 18 publications

On the dynamics of ocean ambient noise: Two decades later

On the dynamics of ocean ambient noise: Two decades later

Computation of the Lyapunov exponents in the compass-gait model under OGY control via a hybrid Poincaré map

Multistability in Horizontal Platform System with and without Time Delays

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