Chow, J. H., et al. (1990). Singular Perturbation Analysis of Large-Scale Power-Systems. International Journal of Electrical Power & Energy Systems, 12(2), 117–126. https://doi.org/10.1016/0142-0615(90)90007-X

Article  Google Scholar 

Connors, B. W. (1984). Initiation of Synchronized Neuronal Bursting in Neocortex. Nature, 310(5979), 685–687. https://doi.org/10.1038/310685a0

Article  CAS  PubMed  Google Scholar 

Crisp, D. N., et al. (2020). Quantifying Epileptogenesis in Rats with Spontaneous and Responsive Brain State Dynamics. Brain Communications, 2(1), fcaa048. https://doi.org/10.1093/braincomms/fcaa048

El Houssaini, K., et al. (2020). The Epileptor Model: A Systematic Mathematical Analysis Linked to the Dynamics of Seizures, Refractory Status Epilepticus, and Depolarization Block. eNeuro, 7,(2). https://doi.org/10.1523/ENEURO.0485-18.2019

Fox, D. M., et al. (2015). Bursting in Neurons and Small Networks (pp. 455–469). Springer.

Google Scholar 

Golubitsky, M., et al. (1985). Singularities and Groups in Bifurcation Theory. Springer-Verlag. Applied Mathematical Sciences, 51, 69.

Goyal, A., et al. (2023). Synchronized Electrical Cardioversion. Statpearls. https://www.ncbi.nlm.nih.gov/pubmed/29489237

Guckenheimer, J., & Holmes, P. (1997). Nonlinear oscillations, dynamical systems, and bifurcations of vector fields (1st 1983 ed.). Springer. Applied Mathematical Sciences, 42.

Ikeda, A., et al. (1999). Focal ictal direct current shifts in human epilepsy as studied by subdural and scalp recording. Brain, 122( Pt 5), 827–838. http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=10355669

Izhikevich, E. M. (2010). Dynamical Systems in Neuroscience. The MIT Press.

Jahangiri, A., & Durand, D. M. (2011). Phase resetting analysis of high potassium epileptiform activity in Ca3 region of the rat hippocampus. International Journal Neural Systems, 21(2), 127–138. https://doi.org/10.1142/S0129065711002705

Article  Google Scholar 

Jirsa, V. K., et al. (2014). On the Nature of Seizure Dynamics. Brain, 137(Pt 8), 2210–2230. https://doi.org/10.1093/brain/awu133

Article  PubMed  PubMed Central  Google Scholar 

Jiruska, P., et al. (2013). Synchronization and Desynchronization in Epilepsy: Controversies and Hypotheses. Journal of Physiology, 591(Pt 4), 787–797. https://doi.org/10.1113/jphysiol.2012.239590

Article  CAS  PubMed  Google Scholar 

Johnson, S. W., et al. (1992). Burst Firing in Dopamine Neurons Induced by N-Methyl-D-Aspartate - Role of Electrogenic Sodium-Pump. Science, 258(5082), 665–667. https://doi.org/10.1126/science.1329209

Article  CAS  PubMed  Google Scholar 

Kikani, J., & Pedrosa Jr, O. A. (1991). Perturbation Analysis of Stress-Sensitive Reservoirs (Includes Associated Papers 25281 and 25292 ). Text, Society of Petroleum Engineers, 6. 1991–09–01. https://doi.org/10.2118/20053-PA

Lagarde, S., et al. (2019). The Repertoire of Seizure Onset Patterns in Human Focal Epilepsies: Determinants and Prognostic Values. Epilepsia, 60(1), 85–95. https://doi.org/10.1111/epi.14604

Article  PubMed  Google Scholar 

Lee, S., et al. (2019). Dc Shifts, High Frequency Oscillations, Ripples and Fast Ripples in Relation to the Seizure Onset Zone. Seizure. https://doi.org/10.1016/j.seizure.2019.05.001

Lytton, W. W. (2008). Computer Modelling of Epilepsy. Nature Reviews Neuroscience, 9(8), 626–637. https://doi.org/10.1038/nrn2416

Article  CAS  PubMed  PubMed Central  Google Scholar 

Ma, J., et al. (2012). Small-Signal Stability Analysis of Microgrid Based on Perturbation Theory.  Asia-Pacific Power and Energy Engineering Conference, 2012, 1–4. https://doi.org/10.1109/appeec.2012.6306946. IEEE.

Marder, E., & Taylor, A. L. (2011). Multiple Models to Capture the Variability in Biological Neurons and Networks. Nature Neuroscience, 14(2), 133–138. https://doi.org/10.1038/nn.2735

Article  CAS  PubMed  PubMed Central  Google Scholar 

Martinez, I., et al. (2004). Perturbation Analysis of Power Systems: Effects of Second- and Third-Order Nonlinear Terms on System Dynamic Behavior. Electric Power Systems Research, 71(2), 159–167. https://doi.org/10.1016/S0378-7796(04)00029-X

Article  Google Scholar 

Merrill, D. R., et al. (2005). Electrical Stimulation of Excitable Tissue: Design of Efficacious and Safe Protocols. Journal of Neuroscience Methods, 141(2), 171–198. S0165–0270(04)00382–6 https://doi.org/10.1016/j.jneumeth.2004.10.020

Morrell, M. J. (2011). Responsive Cortical Stimulation for the Treatment of Medically Intractable Partial Epilepsy. Neurology, 77(13), 1295–1304. https://doi.org/10.1212/WNL.0b013e3182302056

Neuropace Inc. (2008). Responsive Neurostimulation for the Treatment of Epilepsy. Retrieved August 8, 2008, from http://www.neuropace.com/product/overview.html

Perucca, P., et al. (2014). Intracranial Electroencephalographic Seizure-Onset Patterns: Effect of Underlying Pathology. Brain, 137(Pt 1), 183–196. https://doi.org/10.1093/brain/awt299

Article  PubMed  Google Scholar 

Proix, T., et al. (2016). How Do Parcellation Size and Short-Range Connectivity Affect Dynamics in Large-Scale Brain Network Models? NeuroImage, 142, 135–149. https://doi.org/10.1016/j.neuroimage.2016.06.016

Article  PubMed  Google Scholar 

Proix, T., et al. (2018). Predicting the Spatiotemporal Diversity of Seizure Propagation and Termination in Human Focal Epilepsy. Nature Communications, 9(1), 1088. https://doi.org/10.1038/s41467-018-02973-y

Article  CAS  PubMed  PubMed Central  Google Scholar 

Rinzel, J. (1987). A Formal Classification of Bursting Mechanisms in Excitable Systems. Mathematical Topics in Population Biology, Morphogenesis and Neurosciences: Proceedings of an International Symposium Held in Kyoto, November 10–15, 1985 (267–281) edited by Ei Teramoto and Masaya Yumaguti, Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-93360-8_26

Saggio, M. L., et al. (2017) Fast-Slow Bursters in the Unfolding of a High Codimension Singularity and the Ultra-Slow Transitions of Classes. Journal of Mathematical Neuroscience, 7. https://doi.org/10.1186/s13408-017-0050-8

Saggio, M. L., et al. (2020). A Taxonomy of Seizure Dynamotypes. Elife, 9. https://doi.org/10.7554/eLife.55632

Saggio, M. L., & Jirsa, V. (2022). Phenomenological Mesoscopic Models for Seizure Activity. arXiv https://arxiv.org/abs/2007.02783. Accessed October 16 2022.

Stacey, W. C., & Litt, B. (2008). Technology Insight: Neuroengineering and Epilepsy-Designing Devices for Seizure Control. Nature Clinical Practice. Neurology, 4(4), 190–201. https://doi.org/10.1038/ncpneuro0750

Article  CAS  PubMed  PubMed Central  Google Scholar 

Thompson, S. A., et al. (2016). Ictal Infraslow Activity in Stereoelectroencephalography: Beyond the “Dc Shift.” Clinical Neurophysiology, 127(1), 117–128. https://doi.org/10.1016/j.clinph.2015.03.020

Article  CAS  PubMed  Google Scholar 

Vanhatalo, S., et al. (2003). Very Slow Eeg Responses Lateralize Temporal Lobe Seizures: An Evaluation of Non-Invasive Dc-Eeg. Neurology, 60(7), 1098–1104.

Article  CAS  PubMed  Google Scholar 

Wang, H. E., et al. (2023). Delineating Epileptogenic Networks Using Brain Imaging Data and Personalized Modeling in Drug-Resistant Epilepsy. Science Translational Medicine, 15(680), eabp8982. https://doi.org/10.1126/scitranslmed.abp8982

Wendling, F., et al. (2015). Computational Models of Epileptiform Activity. Journal of Neuroscience Methods. https://doi.org/10.1016/j.jneumeth.2015.03.027