Multifractal detrended fluctuation analysis of analog random multiplicative processes

Silva, Leonardo B. M.; Vermelho, M. V. D.; Lyra, M. L.; Viswanathan, G. M.

doi:10.1016/j.chaos.2008.10.027

Cited by 9 publications

(4 citation statements)

References 45 publications

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“…To the authors' knowledge, this is the first attempt to query the mono-or multifractal nature of dynamics in BJT-based circuits of the present kind, even though multifractality has been reported for a more complex circuit with stochastic dynamics. 52 Circuit features predicting chaoticity were searched for by comparing the subsets of circuits generating chaotic and periodic signals at all nodes (33 vs. 46) based on 52 measures, including counts of components, series, parallel and tapped LC combinations, single-and double-transistor topologies, LC tank frequencies, and their relationships. As no significant association was found, the details are not presented, and the view that chaos generation in these circuits involves a complex relationship between circuit structure and component values is reinforced.…”

Section: A Overall Featuresmentioning

confidence: 99%

Atypical transistor-based chaotic oscillators: Design, realization, and diversity

Minati

Frasca

Oświęcimka

et al. 2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In this paper, we show that novel autonomous chaotic oscillators based on one or two bipolar junction transistors and a limited number of passive components can be obtained via random search with suitable heuristics. Chaos is a pervasive occurrence in these circuits, particularly after manual adjustment of a variable resistor placed in series with the supply voltage source. Following this approach, 49 unique circuits generating chaotic signals when physically realized were designed, representing the largest collection of circuits of this kind to date. These circuits are atypical as they do not trivially map onto known topologies or variations thereof. They feature diverse spectra and predominantly anti-persistent monofractal dynamics. Notably, we recurrently found a circuit comprising one resistor, one transistor, two inductors, and one capacitor, which generates a range of attractors depending on the parameter values. We also found a circuit yielding an irregular quantized spike-train resembling some aspects of neural discharge and another one generating a double-scroll attractor, which represent the smallest known transistor-based embodiments of these behaviors. Through three representative examples, we additionally show that diffusive coupling of heterogeneous oscillators of this kind may give rise to complex entrainment, such as lag synchronization with directed information transfer and generalized synchronization. The replicability and reproducibility of the experimental findings are good.

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Section: A Overall Featuresmentioning

confidence: 99%

Atypical transistor-based chaotic oscillators: Design, realization, and diversity

Minati

Frasca

Oświęcimka

et al. 2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Owing to the fact that higher order statistics of the real data does not vanish, thus the real data are probably of non-Gaussian nature. At the present step of our analysis, we assume that the groundwater level fluctuations ψ(t) have fractal and non-Gaussian nature (see for example in [40]). This later property will be more investigated in the next section.…”

Section: Higher Order Spectrummentioning

confidence: 99%

On fractal nature of groundwater level fluctuations due to rainfall process

Joelson

Golder

Beltrame

et al. 2016

Chaos, Solitons & Fractals

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a b s t r a c tHourly resolution time series of groundwater level fluctuations are analyzed after removing the seasonal cycle. It is found that fluctuations of groundwater levels have fractal scaling and a persistent behavior. We show also that groundwater level fluctuations exhibit non-Gaussian heavy tailed probability distribution that is well fitted by the Lévy stable distribution. Implications of the present results on the groundwater system modeling as a fractional Lévy motion and the connection with the anomalous diffusion inside the soil are discussed.

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“…In the present work, we will consider the noise input mðtÞ to be power-law distributed. In order to numerically generate such class of noises, we employed a Langevin differential stochastic process including both additive and multiplicative underlying noise sources governed by the following equation [35][36][37].…”

Section: Power-law Distributed Noise and Its Numerical Generationmentioning

confidence: 99%

Ghost stochastic resonance induced by a power-law distributed noise in the FitzHugh–Nagumo neuron model

Silva

Rosso

Vermelho

et al. 2015

Communications in Nonlinear Science and Numerical Simulation

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Multifractal detrended fluctuation analysis of analog random multiplicative processes

Cited by 9 publications

References 45 publications

Atypical transistor-based chaotic oscillators: Design, realization, and diversity

Atypical transistor-based chaotic oscillators: Design, realization, and diversity

On fractal nature of groundwater level fluctuations due to rainfall process

Ghost stochastic resonance induced by a power-law distributed noise in the FitzHugh–Nagumo neuron model

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