A phenomenological model of EEG based on the dynamics of a stochastic Duffing-van der Pol oscillator network

Ghorbanian, Parham; Ramakrishnan, Suresh; Whitman, Alan M.; Ashrafiuon, Hashem

doi:10.1016/j.bspc.2014.08.013

Cited by 20 publications

(21 citation statements)

References 32 publications

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“…While inspired by the above, the authors were fundamentally motivated to develop models that can better reproduce the significant linear and non-linear characteristics of actual EEG signals. Hence, we proposed a phenomenological model of the EEG based on a coupled system of Duffing—van der Pol oscillators subjected to white noise excitation (Ghorbanian et al, 2015 ). This particular oscillator was selected because the Duffing non-linearity allows a system with only two oscillators capture the major brain frequency spectra and van der Pol non-linearity provides self-excited limit cycle behavior which have been previously reported for each major brain frequency bands (Burke and Paor, 2004 ).…”

Section: Methodsmentioning

confidence: 99%

“…In recent work, the authors proposed a phenomenological model of the EEG signal based on the dynamics of a stochastic, coupled, Duffing- van der Pol oscillator network (Ghorbanian et al, 2015 ). An optimization scheme was adopted to match model output with actual EEG data obtained from healthy subjects in the two distinct resting eyes-open (EO) and eyes-closed (EC) conditions and it was shown that the actual EEG signals in both cases were distinct realizations of the model with qualitatively different non-linear dynamic characteristics.…”

Section: Introductionmentioning

confidence: 99%

“…In the present effort, we improve the model introduced in Ghorbanian et al ( 2015 ) by matching the sample entropy of the model output and EEG signal to capture its complexity. A global optimization routine is employed in order to match the output of with EEG recordings in terms of power spectrum, Shannon entropy, and sample entropy.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stochastic non-linear oscillator models of EEG: the Alzheimer's disease case

Ghorbanian

Ramakrishnan

Ashrafiuon

2015

Front. Comput. Neurosci.

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In this article, the Electroencephalography (EEG) signal of the human brain is modeled as the output of stochastic non-linear coupled oscillator networks. It is shown that EEG signals recorded under different brain states in healthy as well as Alzheimer's disease (AD) patients may be understood as distinct, statistically significant realizations of the model. EEG signals recorded during resting eyes-open (EO) and eyes-closed (EC) resting conditions in a pilot study with AD patients and age-matched healthy control subjects (CTL) are employed. An optimization scheme is then utilized to match the output of the stochastic Duffing—van der Pol double oscillator network with EEG signals recorded during each condition for AD and CTL subjects by selecting the model physical parameters and noise intensity. The selected signal characteristics are power spectral densities in major brain frequency bands Shannon and sample entropies. These measures allow matching of linear time varying frequency content as well as non-linear signal information content and complexity. The main finding of the work is that statistically significant unique models represent the EC and EO conditions for both CTL and AD subjects. However, it is also shown that the inclusion of sample entropy in the optimization process, to match the complexity of the EEG signal, enhances the stochastic non-linear oscillator model performance.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stochastic non-linear oscillator models of EEG: the Alzheimer's disease case

Ghorbanian

Ramakrishnan

Ashrafiuon

2015

Front. Comput. Neurosci.

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“…Next theorem deals with the infinite oscillations of the paths of the coupled nonlinear oscillator (8).…”

Section: The Infinitely Many Zeros Of Coupled Nonlinear Oscillatorsmentioning

confidence: 99%

“…On the other hand, demanded by an increasing number of practical applications (see e.g., [7], [1], [8], and references therein), the numerical simulation of stochastic oscillators has also a high interest.…”

Section: Introductionmentioning

confidence: 99%

On the oscillatory behavior of coupled stochastic harmonic oscillators driven by random forces

Cruz¹,

Jiménez

Biscay

2019

Statistics & Probability Letters

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Efficient Memristive Stochastic Differential Equation Solver

Dong

Primeau

Genov

et al. 2023

Advanced Intelligent Systems

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Herein, an efficient numerical solver for stochastic differential equations based on memristors is presented. The solver utilizes the stochastic switching effect in memristive devices to simulate the generation of a Brownian path and employs iterative Euler method computations within memristive crossbars. The correctness of the solution paths generated by the system is examined by solving the Black–Scholes equations and comparing the paths to analytical solutions. It is found that the absolute error of a 128‐step path is limited to an order of . Herein, the tolerance of the system is also accessed to crossbar nonidealities by comparing the numerical and analytical paths' variation in error. The numerical solver is sensitive to the variation in operating conditions, with the error increasing by , , and as the ambient temperature, wire resistance, and stuck probability of the memristor increase to extreme conditions. The solver is tested on a variety of problems to show its utility for different calculations. And, the resource consumption of the proposed structure built with existing technology is estimated and it is compared with similar iterative solvers. The solver generates a solution with the same level of accuracy from to faster than similar digital or mixed‐signal designs.

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A phenomenological model of EEG based on the dynamics of a stochastic Duffing-van der Pol oscillator network

Cited by 20 publications

References 32 publications

Stochastic non-linear oscillator models of EEG: the Alzheimer's disease case

Stochastic non-linear oscillator models of EEG: the Alzheimer's disease case

On the oscillatory behavior of coupled stochastic harmonic oscillators driven by random forces

Efficient Memristive Stochastic Differential Equation Solver

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