A Gaussian mixture model based cost function for parameter estimation of chaotic biological systems

Shekofteh, Yasser; Jafari, Sajad; Sprott, Julien Clinton; Golpayegani, Seyed Mohammad Reza Hashemi; Almasganj, Farshad

doi:10.1016/j.cnsns.2014.05.028

Cited by 28 publications

(16 citation statements)

References 58 publications

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“…We consider IVP (1) with N 0 ∼ U [5,15] and K ∼ U[90, 110] independent uniformly distributed random variables.…”

Section: A N U S C R I P Tmentioning

confidence: 99%

“…In this context, many authors have introduced stochastic population models to investigate the effect of environmental variability and perturbation [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]. Here, we explore uncertainties present in the logistic model, which is commonly applied in the studies of human, plants and bacterial populations, as well as to evaluate economic growth.…”

Section: Introductionmentioning

confidence: 98%

“…Density functions of the solution of (2) for K ∼ U[90, 110] and N 0 ∼ U[5,15]: f N (q; t) (solid line), and simulated by Monte Carlo (circles); a = 0.5.…”

mentioning

confidence: 99%

“…Relative difference between E[N(t)] and the solution of the simplified equation inFigure 5(a); t ∈ [0, 12]; K ∼ U[90, 110] and N 0 ∼ U[5,15]; a = 0.5; Pdf's of t * for K ∼ U[90, 110] and N 0 ∼ U[5,15]: f t * (dotted line), and simulated by Monte Carlo (circles); a = 0.5.…”

mentioning

confidence: 99%

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On the logistic equation subject to uncertainties in the environmental carrying capacity and initial population density

Dorini

Cecconello

Dorini

2016

Communications in Nonlinear Science and Numerical Simulation

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“…We consider IVP (1) with N 0 ∼ U [5,15] and K ∼ U[90, 110] independent uniformly distributed random variables.…”

Section: A N U S C R I P Tmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

“…Density functions of the solution of (2) for K ∼ U[90, 110] and N 0 ∼ U[5,15]: f N (q; t) (solid line), and simulated by Monte Carlo (circles); a = 0.5.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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On the logistic equation subject to uncertainties in the environmental carrying capacity and initial population density

Dorini

Cecconello

Dorini

2016

Communications in Nonlinear Science and Numerical Simulation

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“…The complex patterns such as the chaotic ones are widely observed when the behavior of biological systems, for example brain and heart, and their responses to different internal and external stimuli are precisely assessed [4,[7][8][9][10][11]. This characteristic is the consequence of complicated interactions within various components of every biological system as well as with its environment.…”

Section: Introductionmentioning

confidence: 99%

Artificial neural network-based modeling of brain response to flicker light

et al. 2015

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Not only does the modeling of dynamical systems, for instance the biological systems, play an important role in the accurate perception and analysis of these systems, but it also makes the prediction and control of their behavior straightforward. The results of multiple researches in the field of the modeling of biological systems have indicated that the chaotic behavior is a prevalent feature of most complex interactive biological systems. Our results demonstrate that the artificial neural network provides us an effective means to model the underlying dynamics of these systems. In this paper, at first, we represent the results of the use of a multilayer feed-forward neural network to model some famous chaotic systems. The specified neural network is trained with the return maps extracted from the time series. We proceed with the paper by evaluating the accuracy and robustness of our model. The ability of the select neural network to model the dynamics of chosen chaotic systems is verified, even in the presence of noise. Afterwards, we model the brain response to the flicker light. It is known that the brain response to some stimuli such as the flicker light recorded as electroretinogram is an exemplar of chaotic behavior. The need remains, however, for realistic modeling of this behavior of the brain. In this paper, we represent the results of the modeling of this chaotic response by utilizing the proposed neural network. The capability of the neural network to model this specific brain response is confirmed.

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Square Root Design for Natural Frequency Module of Dynamic ECG Features—a Preliminary Study

Abdul-Kadir

Safri

Othman

et al. 2019

Cardiovascular Engineering

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A Gaussian mixture model based cost function for parameter estimation of chaotic biological systems

Cited by 28 publications

References 58 publications

On the logistic equation subject to uncertainties in the environmental carrying capacity and initial population density

On the logistic equation subject to uncertainties in the environmental carrying capacity and initial population density

Artificial neural network-based modeling of brain response to flicker light

Square Root Design for Natural Frequency Module of Dynamic ECG Features—a Preliminary Study

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