A wavelet-based tool for studying non-periodicity

Benítez, Rafael; Bolós, Vicente J.; Ramírez, M. E.

doi:10.1016/j.camwa.2010.05.010

Cited by 89 publications

(112 citation statements)

References 16 publications

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“…Moreover, wavelets have been successfully used in the analysis of many chaotic systems [31][32][33]. Non-periodicity as a hallmark of a chaotic behavior could be quantified through scale index analysis [33,34]. Let the continuous wavelet transform (CWT) of a signal 2 fL  with respect to some analyzing wavelet function  be: …”

Section: Resultsmentioning

confidence: 99%

Study of the Transition to Instability in Second-Harmonic Generation with Scale Index Method

Behnia

Ziaei

Khodavirdizadeh

2017

IJOP

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ABSTRACT-The emergence of secondharmonic generation (SHG) is a pivotal issue to the development of nano-optical devices and interfaces. Here, we perform a classical analysis of the SHG dynamics with the aim of determining critical values of the electric field. The signals of the SHG process are nonlinear, so it seems reasonable that chaos theory can be a suitable tool to analyze their dynamics. For this purpose the bifurcation analysis and a new measure known as the scale index were employed. Obtained results show that the dynamics approaches from stable to self-pulsing and eventually to chaos through a perioddoubling route. Moreover, the scale index can detect the critical strength of the electric field, where above it the SHG dynamics is chaotic.

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Section: Resultsmentioning

confidence: 99%

Study of the Transition to Instability in Second-Harmonic Generation with Scale Index Method

Behnia

Ziaei

Khodavirdizadeh

2017

IJOP

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“…The scale index technique was proposed by Benitez [33]. This technique enables the obtaining of information about the periodic nature of generated number series.…”

Section: Scale Index Methodsmentioning

confidence: 99%

Pseudorandom number generator based on Arnold cat map and statistical analysis

Avaroğlu¹

2017

Turk J Elec Eng & Comp Sci

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Pseudorandom number generators (PRNGs) generate random bit streams based on deterministic algorithms.Any bit stream generated with a PRNG will repeat itself at a certain point, and the bit streams will become correlated.As a result, all bit streams generated in this manner are statistically weak. Such weakness leads to a strong connection between PRNGs and chaos, which is characterized by ergodicity, confusion, complexity, sensitivity to initial conditions, and dependence on control parameters. In this study, we introduce a PRNG that generates bit sequences by sampling two Arnold cat map outputs. The statistical randomness of bit streams obtained using this PRNG was verified by statistical analyses such as the NIST test suite, the scale index method, statistical complexity measures, and autocorrelation. The generated bit streams successfully passed all the analytical tests and can be safely used for the many applications of randomness.

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“…In recent years some classical systems, such as the logistic map, Henon map, Bonhoeffer-van der Pol oscillator (Benítez et al, 2010), Rössler system (Akhshani et al, 2014), SMA oscillators and the heartbeat dynamics (Behnia et al, 2013) have been analysed by the Scale index. The wavelet transform of a one-dimensional (1D) signal consists of the development into a basis constructed via solutions like functions called wavelet, using various internal transformations and shifts (Awrejcewicz et al, 2009).…”

Section: A Wavelet-based Scale Indexmentioning

confidence: 99%

Active vibration control of an elevator system using magnetorheological damper actuator

Tusset¹,

Santo²,

Balthazar³

et al. 2017

IJNDC

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Abstract:We investigated the horizontal response of a vertical transportation with nonlinearities under excitation by guide rail deformations. A LQR control strategy was used in order to improve the comfort of passengers. To this end, a magnetorheological damper (MR damper) was used. The control force of the damper is a function of the voltage applied in the coil of the MR damper that is based on the force given by the controller. Numerical simulations were performed to investigate the nonlinear behaviour of the adopted mathematical model. Moreover, other issues such as robustness of the control technique were evaluated considering parametric errors and noise measurement. The results show that the LQR control strategy using MR damper can be effective in reducing the vibration of the vertical transport.Keywords: optimal feedback control; vertical transportation; MR damper; high-speed elevator; parametric uncertainties; wavelet-based scale index; nonlinear model; chaos; LQR control; nonlinear dynamics.

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A wavelet-based tool for studying non-periodicity

Cited by 89 publications

References 16 publications

Study of the Transition to Instability in Second-Harmonic Generation with Scale Index Method

Study of the Transition to Instability in Second-Harmonic Generation with Scale Index Method

Pseudorandom number generator based on Arnold cat map and statistical analysis

Active vibration control of an elevator system using magnetorheological damper actuator

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