zbMATH — the first resource for mathematics

Transition dynamics of epileptic seizures in the coupled thalamocortical network model. (English) Zbl 1397.34075
34C60 Qualitative investigation and simulation of ordinary differential equation models
92C20 Neural biology
34C23 Bifurcation theory for ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C45 Invariant manifolds for ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
Full Text: DOI
[1] Amari, S., Dynamics of pattern formation in lateral-inhibition type neural fields, Biol. Cybern., 27, 77-87, (1997) · Zbl 0367.92005
[2] Baier, G.; Taylor, P. N.; Wang, Y., Understanding epileptiform after-discharges as self-terminating transients, Front. Comput. Neurosci., 11, 25, (2017)
[3] Beenhakker, M. P.; Huguenard, J. R., Neurons that fire together also conspire together: Is normal sleep circuitry hijacked to generate epilepsy?, Neuron., 62, 612, (2009)
[4] Bollimunta, A.; Mo, J.; Schroeder, C. E.; Ding, M., Neuronal mechanisms and attentional modulation of corticothalamic alpha oscillations, J. Neurosci., 31, 4935-4943, (2011)
[5] Bonifazi, P.; Goldin, M.; Picardo, M. A.; Jorquera, I.; Cattani, A.; Bianconi, G.; Repreasa, A.; Ben-Ari, Y.; Cossart, R., GABA\({}_{\text{ergic}}\) hub neurons orchestrate synchrony in developing hippocampal networks, Science, 326, 1419-1424, (2009)
[6] Breakspear, M.; Roberts, J. A.; Terry, J. R.; Rodrigues, S.; Mahant, N.; Robinson, P. A., A unifying explanation of primary generalized seizures through nonlinear brain modeling and bifurcation analysis, Cereb. Cortex, 16, 1296-1313, (2006)
[7] Duan, L.; Fan, D.; Lu, Q., Hopf bifurcation and bursting synchronization in an excitable systems with chemical delayed coupling, Cogn. Neurodyn., 7, 341-349, (2013)
[8] Fan, D.; Wang, Q., Synchronization and bursting transition of the coupled hindmarsh-rose systems with asymmetrical time-delays, Sci. China Technol. Sci., 60, 1019-1031, (2017)
[9] Fan, D.; Liao, F.; Wang, Q., The pacemaker role of thalamic reticular nucleus in controlling spike-wave discharges and spindles, Chaos, 27, 331-343, (2017)
[10] Fan, D.; Wang, Q.; Su, J.; Xi, H., Stimulus-induced transitions between spike-wave discharges and spindles with the modulation of thalamic reticular nucleus, J. Comput. Neurosci., 43, 203-225, (2017)
[11] Fan, D.; Duan, L.; Wang, Q.; Luan, G., Combined effects of feedforward inhibition and excitation in thalamocortical circuit on the transitions of epileptic seizures, Front. Comput. Neurosci., 11, 59, (2017)
[12] Fan, D.; Song, X.; Liao, F., Synchronization of coupled Fitzhugh-Nagumo neurons using self-feedback time delay, Int. J. Bifurcation and Chaos, 28, 1850031-1-15, (2018) · Zbl 1386.34097
[13] Foldvary-Schaefer, N.; Wyllie, E., Textbook of Clinical Neurology, Chapter 52 — epilepsy, 1213-1244, (2007)
[14] Gerrard, P.; Malcolm, R., Mechanisms of modafinil: A review of current research, Neuropsychiatr. Dis. Treat., 3, 349-364, (2007)
[15] Goodfellow, M.; Schindler, K.; Baier, G., Intermittent spike-wave dynamics in a heterogeneous, spatially extended neural mass model, NeuroImage, 55, 920-932, (2011)
[16] Liu, S.; Wang, Q., Transition dynamics of generalized multiple epileptic seizures associated with thalamic reticular nucleus excitability: A computational study, Commun. Nonlin. Sci. Numer. Simul., 52, 203-213, (2017)
[17] Lockman, L. A., Absence, myoclonic, and atonic seizures, Pediatric Clinics of North America, 36, 331, (1989)
[18] Lopes da Silva, F.; Blanes, W.; Kalitzin, S. N.; Parra, J.; Suffczynski, P.; Velis, D. N., Epilepsies as dynamical diseases of brain systems: basic models of the transition between normal and epileptic activity, Epilepsia, 44, 72-83, (2003)
[19] Mayville, C.; Fakhoury, T.; Abou-Khalil, B., Absence seizures with evolution into generalized tonic-clonic activity: clinical and EEG features, Epilepsia, 41, 391-394, (2000)
[20] Meeren, H. K. M.; Pijn, J. P. M.; Van Luijtelaar, E. L. J. M.; Coenen, A. M. L.; Lopes da Silva, F. H., Cortical focus drives widespread corticothalamic networks during spontaneous absence seizures in rats, J. Neurosci., 22, 1480-1495, (2002)
[21] Panayiotopoulos, C. P., Typical absence seizures and their treatment, Arch. Dis. Childhood, 81, 351-355, (1999)
[22] Pepaulis, A.; Luijtelaar, G. V., Models of Seizures and Epilepsy, Chapter 18 — genetic models of absence epilepsy in the rat, 233-248, (2006), Academic Press
[23] Robinson, P. A.; Rennie, C. J.; Rowe, D. L., Dynamics of large-scale brain activity in normal arousal states and epileptic seizures, Phys. Rev. E: Statist. Nonlin. Soft Matt. Phys., 65, 041924, (2002)
[24] Rodrigues, S.; Terry, J. R.; Breakspear, M., On the genesis of spike-wave activity in a mean-field model of human brain activity, Phys. Lett. A, 355, 352-357, (2005)
[25] Shih, T. T.; Hirsch, L. J., Tonic-absence seizures: an underrecognized seizure type, Epilepsia, 44, 461-465, (2003)
[26] Suffczynski, P.; Kalitzin, S.; Pfurtscheller, G.; Lopes da Silva, F. H., Computational model of thalamo-cortical networks: dynamical control of alpha rhythm in relation to focal attention, Int. J. Psychophysiol., 43, 25-40, (2001)
[27] Taylor, P. N.; Baier, G., A spatially extended model for macroscopic spike-wave discharges, J. Comput. Neurosci., 31, 679-684, (2011)
[28] Taylor, P. N.; Wang, Y.; Goodfellow, M.; Dauwels, J.; Modeller, F.; Steohani, U.; Baier, G., A computational study of stimulus driven epileptic seizure abatement, PLoS One, 9, e114316, (2014)
[29] Timofeev, I.; Steriade, M., Neocortical seizures: initiation, development and cessation, Neuroscience, 123, 299-336, (2004)
[30] Wang, Y.; Goodfellow, M.; Taylor, P. N.; Baier, G., Phase space approach for modeling of epileptic dynamics, Phys. Rev. E: Statist. Nonlin. Soft Matt. Phys., 85, 061918, (2012)
[31] Wang, Z.; Wang, Q., Effect of the coordinated reset stimulations on controlling absence seizure, Sci. China Technol. Sci., 60, 1-10, (2017)
[32] Zhang, H.; Xiao, P., Seizure dynamics of coupled oscillators with epileptor field model, Int. J. Bifurcation and Chaos, 28, 1850041-1-19, (2018) · Zbl 1388.34053
[33] Ziburkus, J.; Cressman, J. R.; Barreto, E.; Schiff, S. J., Interneuron and pyramidal cell interplay during in vitro seizure-like event, Neurophysiol., 95, 3948-3954, (2006)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.