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'''Hilbert spectral analysis''' is a signal analysis method applying the [[Hilbert transform]] to compute the [[instantaneous fr ...the amplitude can be contoured on the frequency-time plane. This frequency-time distribution of the amplitude is designated as the Hilbert amplitude spectr ...

...he coefficients are referred to as '''Wiener kernels'''. The terms of the series are orthogonal (uncorrelated) with respect to a statistical input of [[whit ...the output to the entire history of system input at any time. The Wiener series has been applied mostly to the identification of biological systems, especi ...

...onance''' is the occurrence of [[resonance]] in a [[nonlinear system]]. In nonlinear resonance the system behaviour – [[resonance frequency|resonance frequencie ...s with the [[natural frequency|eigen-frequency]] of the system (linear and nonlinear resonance correspondingly). Vibrational modes can interact in a [[resonant ...

...mating linear filters in a [[linear-nonlinear-Poisson cascade model|linear-nonlinear-Poisson (LNP)]] cascade model. Unlike STA, the STC can be used to identify STC analysis identifies the stimulus features affecting a neuron's response via an eigen ...

...eaching/neurostat-fall13/papers/Chichilnisky-2001.pdf A simple white noise analysis of neuronal light responses.] {{webarchive|url=https://web.archive.org/web/ [[Image:LNPModelDiagram.png|right|thumb|300px|The Linear-Nonlinear-Poisson Cascade Model]] ...

...oothing algorithm.<ref name=":2">{{cite journal|title = A multidimensional nonlinear edge-preserving filter for magnetic resonance image restoration|journal = I == Nonlinear analyser == ...

...w( x_1, x_2, t ) </math> and the following standard notation of [[complex analysis]] is used: <math>\Re</math> is the [[real and imaginary parts|real part]], ==Relation to other nonlinear integrable equations== ...

...nce]]s. The method can be described as the [[FTCS scheme|FTCS (forward in time, centered in space) scheme]] with a numerical dissipation term of 1/2. One == Extensions to Nonlinear Problems == ...

...s, where multiple observations are made on collections of individuals over time.]] ...multivariate linear model, also known as GMANOVA (Generalized Multivariate Analysis-Of-Variance).<ref>{{cite book ...

...by Means of S-estimators, from the book: Robust and nonlinear time series analysis, pages 256–272, 1984</ref> ...

{{Distinguish|Multiresolution analysis}} In [[mathematics]] and [[physics]], '''multiple-scale analysis''' (also called the '''method of multiple scales''') comprises techniques u ...

...4</ref> is an American mathematician, specializing in nonlinear functional analysis and differential equations. ...0.1090/S0002-9904-1968-11988-3|title=The topological degree for noncompact nonlinear mappings in Banach spaces|year=1968|last1=Browder|first1=Felix E.|last2=Nus ...

...e formed by removing the trend component. This approach is utilized in the analysis of the [[trend-stationary process]]. ...|first6=Sirak |last7=Hovhannisyan |first7=Narek |title=An Enterprise Time Series Forecasting System for Cloud Applications Using Transfer Learning |journal= ...

...e]] of a dynamical system can be reconstructed from a single observed time series of the system, <math>X</math>. This reconstructed or ''shadow manifold'' <m ...71/journal.pone.0018295 | doi-access=free | title=Generalized Theorems for Nonlinear State Space Reconstruction | year=2011 | last1=Deyle | first1=Ethan R. | la ...

...reams are fed into this distorted channel model. The receiver compares the time response with the actual received signal and determines the most likely sig ...ision criterion<ref>G. Bosco, P. Poggiolini, and M. Visintin, "Performance Analysis of MLSE Receivers Based on the Square-Root Metric," J. Lightwave Technol. 2 ...

...aldrikian |author5=J. Doyne Farmer |title=Testing for nonlinearity in time series: the method of surrogate data ...If the value of the statistic is significantly different for the original series than for the surrogate set, the null hypothesis is rejected and non-lineari ...

...=Forward-Backward Stochastic Differential Equations and their Applications|series=Lecture Notes in Mathematics |volume=1702 |url=https://link.springer.com/bo ...066-8}}</ref> and by [[Étienne Pardoux]] and [[Shige Peng]] in 1990 in the nonlinear case.<ref>{{cite journal|last1=Pardoux|first1=Etienne|last2=Peng|first2=Shi ...

...or fields and represent their flows as infinite [[Volterra series]]. These series, at first introduced as purely formal expansions, are then shown to converg Iterating one more time the procedure, we arrive to ...

{{Short description|Numerical analysis procedure}} ...3,M1 Analysis of Numerical Methods by E. Isaacson, H. B. Keller]</ref> The analysis is based on the [[Fourier decomposition]] of [[numerical error]] and was de ...

| fields = [[Nonlinear Systems]]<br />[[Complex Networks]]<br />[[Chaos Theory]] ...[Control of chaos|control theory]], [[Bifurcation theory|bifurcations]], [[nonlinear dynamics]], [[complex systems]], etc.<ref name="CUHK - undated - Guanrong C ...