Estimation of fixed points for nonlinear time series

Mohammadi, Shahriar; Abbasinezhad, H

doi:10.1002/cplx.21487

Cited by 2 publications

(3 citation statements)

References 18 publications

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“…In the surrogate datatest, the IAAFT is applied to preserve the probability density function and the correlation structure (and therefore the power spectrum) of the original data, by iteratively minimizing the deviation. The main procedure of the adopted algorithm is given below . A sorted record of the original spatial series

true{s_{n} true}

and the squared amplitudes of its Fourier transform,

S_{k}^{2} = {| \sum_{n = 0}^{N - 1} e^{i 2 π k n / n} |}^{2}

are saved. The data is randomly shuffled (without substitution)

({}|, s_{n}^{(0)})

to corrupt any nonlinear associations and correlations. The Fourier transform of

({}|, s_{n}^{(i)})

is calculated and its squared amplitude is substituted by

S_{k}^{2}

.…”

Section: Methodology For Nonlinear Analysis Of Spatial Seriesmentioning

confidence: 99%

“…Dhanya and Kumar have collected daily rainfall data of three regions with contrasting characteristics to study the dynamical properties of the data. In , a method based on polynomial regression has been provided for identifying fixed points in dynamic systems. In , two chaotic indicators namely the correlation dimension and the Lyapunov exponent methods have been applied for the daily river flow of Kizilirmak River.…”

Section: Introductionmentioning

confidence: 99%

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Chaos and complexity in mine grade distribution series detected by nonlinear approaches

Aghababa

Sharif

2016

Complexity

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In this article, the underlying dynamics of treating grade distribution is interpreted as a chaotic system instead of a stochastic system for a better understanding. Here, we study the behavior of grade distribution spatial series acquired at the Chadormalu mine in Bafgh city of Iran to distinguish the possible existence of low‐dimensional deterministic chaos. This work applies a variety of nonlinear techniques for detecting the chaotic nature of the grade distribution spatial series and adopts a nonlinear prediction method for predicting the future of the grade distributions. First, the delay time dimension is computed using auto mutual information function to reconstruct the strange attractors. Then, the dimensionality of the trajectories is obtained using Cao's method and, correspondingly, the correlation dimension method is adopted to quantify the embedding dimension. The low embedding dimensions achieved from these methods show the existence of low dimensional chaos in the mining data. Next, the high sensitivity to initial conditions is evaluated using the maximal Lyapunov exponent criterion. Positive Lyapunov exponents obtained demonstrate the exponential divergence of the trajectories and hence the unpredictability of the data. Afterward, the nonlinear surrogate data test is done to further verify the nonlinear structure of the grade distribution series. This analysis provides considerable evidence for the being of low‐dimensional chaotic dynamics underlying the mining spatial series. Lastly, a nonlinear prediction scheme is carried out to predict the grade distribution series. Some computer simulations are presented to illustrate the efficiency of the applied nonlinear tools. © 2016 Wiley Periodicals, Inc. Complexity 21: 355–369, 2016

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true{s_{n} true}

and the squared amplitudes of its Fourier transform,

S_{k}^{2} = {| \sum_{n = 0}^{N - 1} e^{i 2 π k n / n} |}^{2}

are saved. The data is randomly shuffled (without substitution)

({}|, s_{n}^{(0)})

to corrupt any nonlinear associations and correlations. The Fourier transform of

({}|, s_{n}^{(i)})

is calculated and its squared amplitude is substituted by

S_{k}^{2}

.…”

Section: Methodology For Nonlinear Analysis Of Spatial Seriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Chaos and complexity in mine grade distribution series detected by nonlinear approaches

Aghababa

Sharif

2016

Complexity

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show abstract

“…NNs with delays have been successfully applied to signal processing, pattern recognition, optimization solvers, and intelligence control. Much work has been done on the delayed NNs, including local and global stability, bifurcation, chaos, and synchronization . From the point of view of nonlinear dynamics, the study of NNs with delays is useful and important to solve problems both theoretically and practically.…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis of a delayed six‐neuron BAM network

Huang

Cao

et al. 2015

Complexity

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In this article, a simplified bidirectional associative memory network with delays involving six neurons is considered. By analyzing the distribution of roots of the characteristic equation for linearized system regarding the sum of delay as a bifurcation parameter, we obtain the condition of the occurrence for Hopf bifurcation. It reveals that Hopf bifurcation occurs when the sum of the delay passes through a critical value. The direction and the stability of the bifurcating periodic solution are determined by applying the normal form theory and center manifold theorem. Finally, a numerical example is used to illustrate the validity of theoretical results obtained. V C 2015 Wiley Periodicals, Inc. Complexity 000: 00-00, 2015

show abstract

Estimation of fixed points for nonlinear time series

Cited by 2 publications

References 18 publications

Chaos and complexity in mine grade distribution series detected by nonlinear approaches

Chaos and complexity in mine grade distribution series detected by nonlinear approaches

Dynamical analysis of a delayed six‐neuron BAM network

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