If you are interested in an online/dynamic modeling, I recommend to use a state-space autoregressive model:

• https://pdfs.semanticscholar.org/d327/45a36d5bfcc46bde19e4bb4b5b5b4fe33198.pdf
• https://www.google.fr/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwj546z76fbTAhVHBMAKHZKdAZsQFggrMAA&url=http%3A%2F%2Fwww.springer.com%2Fcda%2Fcontent%2Fdocument%2Fcda_downloaddocument%2F9784431553021-c2.pdf%3FSGWID%3D0-0-45-1498388-p177033534&usg=AFQjCNHJ6rvaWHp_IRZkeEi_sw7wNEviWQ
• https://www.google.fr/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&cad=rja&uact=8&ved=0ahUKEwjxoPOv6PbTAhWnJMAKHSaaAacQFgg3MAI&url=http%3A%2F%2Fbayanbox.ir%2Fview%2F2429911751174223415%2FIntroduction-to-Time-Series-Modeling-by-Kitagawa.pdf&usg=AFQjCNF9q1I_U1gboTctYcU-s1aVP58pPw

Neverthless, so-called DDEs (Delay Differential Equations), which typically derived from ODEs, may be successfully applied  to non-linear dynamical classification in Electroencephalography:

• https://www.researchgate.net/profile/Claudia_Lainscsek/publication/264986093_Delay_Differential_Analysis_of_Electroencephalographic_Data/links/5429ba1c0cf27e39fa8e67bc.pdf
• https://pdfs.semanticscholar.org/dd69/bd142aeaba40c60b9063a99274ef2b4f4206.pdf

Regards

Article Delay Differential Analysis of Electroencephalographic Data

If you use a software package that has a really good and well State Space function, you may be able to avoid some of this, but the vast majority of such functions in R packages for signal processing, require you to jump into the details at some point.

EEG-signal analysis simultaneously requires to link/correlate both spatial and temporal dimensions:

• https://www.researchgate.net/profile/Bertram_Opitz/publication/13610714_A_new_concept_for_EEGMEG_signal_analysis_Detection_of_interacting_spatial_modes/links/0912f50b48b9e5526e000000.pdf
• http://medi.uni-oldenburg.de/download/docs/paper/riedel/journal_articles/Hutt2003PD_AnalysisAndModelingOfQuasiStationaryMultivariateTimeSeries.pdf

This remains a challenge when processing in real-time (streaming) but some solutions exist nowadays:

• https://hal.archives-ouvertes.fr/hal-00621251/document
• http://www.cs.colostate.edu/eeg/main/sites/default/files/forney_poster_cebl_FRNG-2015.pdf

Some additional sources of information:

• https://www.hindawi.com/journals/cin/2011/935364/
• https://www.google.fr/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&cad=rja&uact=8&ved=0ahUKEwiqh8apkYHUAhWD1xoKHfu2DHoQFgg-MAI&url=https%3A%2F%2Fwww.jstatsoft.org%2Farticle%2Fview%2Fv033i05%2Fv33i05.pdf&usg=AFQjCNFwB8Jrxu8rF3rkO6qXMAM1M5y4vA
• https://www.researchgate.net/profile/Scott_Makeig/publication/257015229_Linking_brain_mind_and_behavior/links/565ba38908ae4988a7ba8621.pdf

Hoping it will be helpfull

Article A new concept for EEG/MEG signal analysis: Detection of inte...

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Article Linking brain, mind, and behavior

How event related potentials can be mapped to the characterization of brain dynamics ? Is it possible to map for any EEG parameter to model and map? 

I was thinking it may be possible to perform a polynomial fit around the peaks (locally) and then look at the dynamics within the neighbourhoods of the peaks.  Of course, you'd need to low pass filter the signal first.

I have no idea if it would work, or what information could be found (I've just started my PhD 3 months ago, not even confirmed yet), but I do know that polynomials are easy to differentiate and integrate.  :)

An alternative to polynomial interpolation may be a spline-based interpolation. The latter has very often the advantage of a lower computational cost.

From a signal processing point of view, the event-related potential mapping may be thought of as a "robust smoothing with missing values" problem for which efficient solutions exist. Follow:

• http://www.macs.hw.ac.uk/~iain/research/GLAM/CSDA_2006/CSDA.pdf (see Figure 4)
• https://pdfs.semanticscholar.org/ac93/a8c601c928d003c739ef7525b1748fc8dbb8.pdf

This problem may possibly be reduced to robust smoothing of 2D gridded data by means of conformal mapping techniques.

he EEG signal itself has several components separated by frequency. Delta waves are characteristic of deep sleep and are high amplitude waves in the frequency range 0≤f≤4 Hz. Theta waves occur within the 4-8 Hz frequency band during meditation, idling, or drowsiness. Alpha waves have frequency range 8-14 Hz and take place while relaxing or reflecting. Another way to boost alpha waves is to close the eyes. Beta waves reside in the 13-30 Hz frequency band and are characteristic of the user being alert or active. They become present while the user is concentrating. Gamma waves in the 30-100 Hz range occur during sensory processing of sound and sight. Lastly, mu waves occur in the 8-13 Hz frequency range while motor neurons are at rest.he EEG signal itself has several components separated by frequency. Delta waves are characteristic of deep sleep and are high amplitude waves in the frequency range 0≤f≤4 Hz. Theta waves occur within the 4-8 Hz frequency band during meditation, idling, or drowsiness. Alpha waves have frequency range 8-14 Hz and take place while relaxing or reflecting. Another way to boost alpha waves is to close the eyes. Beta waves reside in the 13-30 Hz frequency band and are characteristic of the user being alert or active. They become present while the user is concentrating. Gamma waves in the 30-100 Hz range occur during sensory processing of sound and sight. Lastly, mu waves occur in the 8-13 Hz frequency range while motor neurons are at rest.Hope it may be possible