1. Fisher, R. S. et al. ILAE official report: a practical clinical definition of epilepsy. Epilepsia 55, 475–482 (2014).

2. Jiruska, P. et al. Synchronization and desynchronization in epilepsy: controversies and hypotheses. J. Physiol. (Lond.) 591, 787–797 (2013).

3. Jirsa, V. K., Stacey, W. C., Quilichini, P. P., Ivanov, A. I. & Bernard, C. On the nature of seizure dynamics. Brain 137, 2210–2230 (2014).

4. Lopes da Silva, F. Epilepsy as a disease of the dynamics of neuronal networks: models and predictions. In Seizure Prediction in Epilepsy: From Basic Mechanisms to Clinical Applications (eds. Schelter, B., Timmer, J. & Schulze-Bonhage, A.) 97–107 (Wiley-VCH, Weinheim, Germany, 2008).

5. Beghi, E. et al. Recommendation for a definition of acute symptomatic seizure. Epilepsia 51, 671–675 (2010).

6. Breakspear, M. et al. A unifying explanation of primary generalized seizures through nonlinear brain modeling and bifurcation analysis. Cereb. Cortex 16, 1296–1313 (2006).

7. Lopes da Silva, F. et al. Epilepsies as dynamical diseases of brain systems: basic models of the transition between normal and epileptic activity. Epilepsia 44 (Suppl 12), 72–83 (2003).

8. de Curtis, M. & Avanzini, G. Interictal spikes in focal epileptogenesis. Prog. Neurobiol. 63, 541–567 (2001).

9. Avoli, M., de Curtis, M. & Köhling, R. Does interictal synchronization influence ictogenesis? Neuropharmacology 69, 37–44 (2013).

10. Barbarosie, M. & Avoli, M. CA3-driven hippocampal-entorhinal loop controls rather than sustains in vitro limbic seizures. J. Neurosci. 17, 9308–9314 (1997).

11. Karoly, P. J. et al. Interictal spikes and epileptic seizures: their relationship and underlying rhythmicity. Brain 139, 1066–1078 (2016).

12. Avoli, M. & de Curtis, M. GABAergic synchronization in the limbic system and its role in the generation of epileptiform activity. Prog. Neurobiol. 95, 104–132 (2011).

13. Huberfeld, G. et al. Glutamatergic pre-ictal discharges emerge at the transition to seizure in human epilepsy. Nat. Neurosci. 14, 627–634 (2011).

14. Rinaldi, S. & Scheffer, M. Geometric analysis of ecological models with slow and fast processes. Ecosystems 3, 507–521 (2000).

15. Scheffer, M. et al. Anticipating critical transitions. Science 338, 344–348 (2012).

16. Scheffer, M. et al. Early-warning signals for critical transitions. Nature 461, 53–59 (2009).

17. Draguhn, A., Traub, R. D., Schmitz, D. & Jefferys, J. G. Electrical coupling underlies high-frequency oscillations in the hippocampus in vitro. Nature 394, 189–192 (1998).

18. Jiruska, P. et al. High-frequency network activity, global increase in neuronal activity, and synchrony expansion precede epileptic seizures in vitro. J. Neurosci. 30, 5690–5701 (2010).

19. Lopes, M. A., Lee, K. E. & Goltsev, A. V. Neuronal network model of interictal and recurrent ictal activity. Phys. Rev. E 96, 062412 (2017).

20. Kalitzin, S., Velis, D., Suffczynski, P., Parra, J. & da Silva, F. L. Electrical brain-stimulation paradigm for estimating the seizure onset site and the time to ictal transition in temporal lobe epilepsy. Clin. Neurophysiol. 116, 718–728 (2005).

21. Scheffer, M. & Carpenter, S. R. Catastrophic regime shifts in ecosystems: linking theory to observation. Trends Ecol. Evol. 18, 648–656 (2003).

22. Hawkins, C. A. & Mellanby, J. H. Limbic epilepsy induced by tetanus toxin: a longitudinal electroencephalographic study. Epilepsia 28, 431–444 (1987).

23. Jiruska, P. et al. Epileptic high-frequency network activity in a model of non-lesional temporal lobe epilepsy. Brain 133, 1380–1390 (2010).

24. Cook, M. J. et al. Prediction of seizure likelihood with a long-term, implanted seizure advisory system in patients with drug-resistant epilepsy: a first-in-man study. Lancet Neurol. 12, 563–571 (2013).

25. Wendling, F., Bartolomei, F., Bellanger, J. J. & Chauvel, P. Epileptic fast activity can be explained by a model of impaired GABAergic dendritic inhibition. Eur. J. Neurosci. 15, 1499–1508 (2002).

26. Fröhlich, F., Sejnowski, T. J. & Bazhenov, M. Network bistability mediates spontaneous transitions between normal and pathological brain states. J. Neurosci. 30, 10734–10743 (2010).

27. de Curtis, M. & Avoli, M. Initiation, Propagation, and Termination of Partial (Focal) Seizures. Cold Spring Harb. Perspect. Med. 5, a022368 (2015).

28. Suffczynski, P. et al. Dynamics of epileptic phenomena determined from statistics of ictal transitions. IEEE Trans. Biomed. Eng. 53, 524–532 (2006).

29. Scheffer, M. Critical Transitions in Nature and Society (Princeton University Press, Princeton, NJ, USA, 2009).

30. Kramer, M. A. et al. Human seizures self-terminate across spatial scales via a critical transition. Proc. Natl. Acad. Sci. USA 109, 21116–21121 (2012).

31. van de Leemput, I. A. et al. Critical slowing down as early warning for the onset and termination of depression. Proc. Natl. Acad. Sci. USA 111, 87–92 (2014).

32. Jiruska, P., Mormann, F. & Jefferys, J.G.R. Neuronal and network dynamics preceding experimental seizures. in R ecent Advances in Predicting and Preventing Epileptic Seizures (eds. Tetzlaff, R. & Elger, C.E.) 16–29 (2013).

33. Blauwblomme, T., Jiruska, P. & Huberfeld, G. Mechanisms of ictogenesis. Int. Rev. Neurobiol. 114, 155–185 (2014).

34. Jensen, M. S. & Yaari, Y. The relationship between interictal and ictal paroxysms in an in vitro model of focal hippocampal epilepsy. Ann. Neurol. 24, 591–598 (1988).

35. Gotman, J. & Marciani, M. G. Electroencephalographic spiking activity, drug levels, and seizure occurrence in epileptic patients. Ann. Neurol. 17, 597–603 (1985).

36. Avoli, M. et al. Specific imbalance of excitatory/inhibitory signaling establishes seizure onset pattern in temporal lobe epilepsy. J. Neurophysiol. 115, 3229–3237 (2016).

37. de Curtis, M., Librizzi, L. & Biella, G. Discharge threshold is enhanced for several seconds after a single interictal spike in a model of focal epileptogenesis. Eur. J. Neurosci. 14, 174–178 (2001).

38. Muldoon, S. F. et al. GABAergic inhibition shapes interictal dynamics in awake epileptic mice. Brain 138, 2875–2890 (2015).

39. Avoli, M. et al. Synchronous GABA-mediated potentials and epileptiform discharges in the rat limbic system in vitro. J. Neurosci. 16, 3912–3924 (1996).

40. Bikson, M., Fox, J. E. & Jefferys, J. G. Neuronal aggregate formation underlies spatiotemporal dynamics of nonsynaptic seizure initiation. J. Neurophysiol. 89, 2330–2333 (2003).

41. Suffczynski, P., Kalitzin, S. & Lopes Da Silva, F. H. Dynamics of non-convulsive epileptic phenomena modeled by a bistable neuronal network. Neuroscience 126, 467–484 (2004).

42. Benjamin, O. et al. A phenomenological model of seizure initiation suggests network structure may explain seizure frequency in idiopathic generalised epilepsy. J. Math. Neurosci. 2, 1 (2012).

43. Naze, S., Bernard, C. & Jirsa, V. Computational modeling of seizure dynamics using coupled neuronal networks: factors shaping epileptiform activity. PLoS Comput. Biol. 11, e1004209 (2015).

44. Kim, J. W., Roberts, J. A. & Robinson, P. A. Dynamics of epileptic seizures: evolution, spreading, and suppression. J. Theor. Biol. 257, 527–532 (2009).

45. Jensen, M. S. & Yaari, Y. Role of intrinsic burst firing, potassium accumulation, and electrical coupling in the elevated potassium model of hippocampal epilepsy. J. Neurophysiol. 77, 1224–1233 (1997).

46. Traynelis, S. F. & Dingledine, R. Potassium-induced spontaneous electrographic seizures in the rat hippocampal slice. J. Neurophysiol. 59, 259–276 (1988).

47. Williams, P. A. et al. Development of spontaneous recurrent seizures after kainate-induced status epilepticus. J. Neurosci. 29, 2103–2112 (2009).

48. Baud, M. O. et al. Multi-day rhythms modulate seizure risk in epilepsy. Nat. Commun. 9, 88 (2018).

49. Saggio, M. L., Spiegler, A., Bernard, C. & Jirsa, V. K. Fast-slow bursters in the unfolding of a high codimension singularity and the ultra-slow transitions of classes. J. Math. Neurosci. 7, 7 (2017).