Research on Bifurcation of a Class of Cortical EEG Model with Time Delay

Abstract

Abstract: The bifurcation characters of a cortical-model with bidirectional time delays were studied, proposed by Robinson, et al. before. Considering transmitting delay between excitatory and inhibitory populations, the stability, bifurcation characters and bifurcation region were achieved. The relationship of cortical potential spectrum density and transmit delay was analyzed when white noise was introduced. Result shows that time delay between different population acts as an important role of model’s dynamic characters and stability, and numerical simulation verifies the theoretical analysis. This research shows the importance of transmit delay in cortical-model, and provides theoretical illustration for further research of epileptic seizure.

Key words: EEG model, time delay, Hopf bifurcation, stability, epilepsy

CLC Number:

TP.391.9

Li Chunsheng, Zhang Xue. Research on Bifurcation of a Class of Cortical EEG Model with Time Delay[J]. Journal of System Simulation, 2015, 27(12): 3063-3069.

References

[1] Jansen B H, Rit V G.Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns[J]. Biological Cybernetics (S0340-1200), 1995, 73(4): 357-366.
[2] 王兴元, 骆超, 谭贵霖. EEG动力学模型中混沌现象的研究[J]. 生物物理学报, 2005, 21(4): 307-316.
[3] 张锦, 黄诗苹, 朱尚武, 等. 基于脑电同步的嗅觉仿生模型优化研究[J]. 系统仿真学报, 2013, 25(5): 907-910.
[4] Freeman W.Mass Action in the Nervous System [M]. New York, USA: Academic Press, 1975.
[5] Lopes da Silva F, Hoecks A, Smits H, et al. Model of brain rhythmic activity: the alpha-rhythm of the thalamus [J]. Kybernetik (S0023-5946), 1974, 15(1): 27-37.
[6] Robinson P, Rennie C, Rowe D.Dynamics of large-scale brain activity in normal arousal states and epileptic seizures[J]. Physical Review E (S1539-3755), 2002, 65(4).
[7] Xu D, Principe J.Dyanmical analysis of neural oscillators in an olfactory cortex model[J]. IEEE Trans on Neural Networks (S1045-9227), 2004, 15(5): 1053-1062.
[8] Rodrigues S, Goncalves J, Terry J.Existence and stability of limit cycles in a macroscopic neuronal population model[J]. Physica D (S0167-2789), 2007, 233(1): 39-65.
[9] Aarabi A, He B.Seizure prediction in hippocampal and neocortical epilepsy using a model-based approach[J]. Clinical Neurophysiology (S1388-2457), 2014, 125(5): 930-940.
[10] Shampine L F, Thompson S.Solving DDEs in MATLAB[J]. Applied Numerical Mathematics (S0168-9274), 2001, 37(4): 441-458.
[11] Nunez P L, Srinivasan R.Electric fields of the brain: The neurophysics of EEG [Z]. Oxford: Oxford University Press, 2006: 5-8.
[12] Winterhalder M, Maiwald T, Voss H U, et al. The seizure prediction characteristic: A general framework to assess and compare seizure prediction methods[J]. Epilepsy Behavior (S1525-5050), 2003, 4(3): 318-325.
[13] Jirsa V K, Stacey W C, Quilichini P P, et al.On the nature of seizure dynamics[J]. Brain (S0006-8950), 2014, 137(8): 2210-2230.

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