Transition dynamics and adaptive synchronization of time-delay interconnected corticothalamic systems via nonlinear control

被引：20
作者：
Fan, Denggui [1 ,2 ]
Zhang, Liyuan [3 ]
Wang, Qingyun [3 ]
机构：
[1] Univ Sci & Technol Beijing, Sch Math & Phys, Beijing 100083, Peoples R China
[2] Univ Sci & Technol Beijing, Beijing Key Lab Knowledge Engn Mat Sci, Beijing, Peoples R China
[3] Beihang Univ, Dept Dynam & Control, Beijing 100191, Peoples R China
来源：
NONLINEAR DYNAMICS | 2018年 / 94卷 / 04期
基金：
中国博士后科学基金; 国家重点研发计划; 中国国家自然科学基金;
关键词：
Corticothalamic model; Time delay; Transition dynamics; Adaptive synchronization; Nonlinear control; SPIKE-WAVE DISCHARGES; HINDMARSH-ROSE NEURONS; ABSENCE SEIZURES; SLEEP SPINDLES; NETWORK MODEL; OSCILLATIONS; EPILEPSY;
D O I：
10.1007/s11071-018-4526-1
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
A modified corticothalamic (MCT) system with multiple delays for epileptic absence seizures is taken as a study object. Synchronization transition dynamics of two time-delay interconnected MCT systems via nonlinear control is investigated in this paper. Both the intrinsic delays in a single MCT system and the coupling delays between two MCT systems are considered. When there is no control, it is found that the occurrences of synchronization are dependent on the specific deviations of intrinsic delays and also correlated with the rhythmic periods of oscillations for the two MCT subsystems. To obtain the synchronous state transitions irrespective of the intrinsic delays, based on the Lyapunov stability theory, we propose a nonlinear adaptive control schemes with respect to the coupling delays. The numerical simulation results show the effectiveness of the designed control method.
引用
收藏
页码：2807 / 2825
页数：19
相关论文
共 45 条
  • [1] Low-frequency (<1 Hz) oscillations in the human sleep electroencephalogram
    Achermann, P
    Borbely, AA
    [J]. NEUROSCIENCE, 1997, 81 (01) : 213 - 222
  • [2] The K-complex: Its slow (<1-Hz) rhythmicity and relation to delta waves
    Amzica, F
    Steriade, M
    [J]. NEUROLOGY, 1997, 49 (04) : 952 - 959
  • [3] [Anonymous], 1969, The Physiopathogenesis of the Epilepsies
  • [4] A unifying explanation of primary generalized seizures through nonlinear brain modeling and bifurcation analysis
    Breakspear, M.
    Roberts, J. A.
    Terry, J. R.
    Rodrigues, S.
    Mahant, N.
    Robinson, P. A.
    [J]. CEREBRAL CORTEX, 2006, 16 (09) : 1296 - 1313
  • [5] Childhood absence epilepsy: Behavioral, cognitive, and linguistic comorbidities
    Caplan, Rochelle
    Siddarth, Prabha
    Stahl, Lesley
    Lanphier, Erin
    Vona, Pamela
    Gurbani, Suresh
    Koh, Susan
    Sankar, Raman
    Shields, W. Donald
    [J]. EPILEPSIA, 2008, 49 (11) : 1838 - 1846
  • [6] Critical Roles of the Direct GABAergic Pallido-cortical Pathway in Controlling Absence Seizures
    Chen, Mingming
    Guo, Daqing
    Li, Min
    Ma, Tao
    Wu, Shengdun
    Ma, Jingling
    Cui, Yan
    Xia, Yang
    Xu, Peng
    Yao, Dezhong
    [J]. PLOS COMPUTATIONAL BIOLOGY, 2015, 11 (10)
  • [7] Bidirectional Control of Absence Seizures by the Basal Ganglia: A Computational Evidence
    Chen, Mingming
    Guo, Daqing
    Wang, Tiebin
    Jing, Wei
    Xia, Yang
    Xu, Peng
    Luo, Cheng
    Valdes-Sosa, Pedro A.
    Yao, Dezhong
    [J]. PLOS COMPUTATIONAL BIOLOGY, 2014, 10 (03)
  • [8] Waves, bumps, and patterns in neural field theories
    Coombes, S
    [J]. BIOLOGICAL CYBERNETICS, 2005, 93 (02) : 91 - 108
  • [9] A Thalamocortical Neural Mass Model of the EEG during NREM Sleep and Its Response to Auditory Stimulation
    Costa, Michael Schellenberger
    Weigenand, Arne
    Ngo, Hong-Viet V.
    Marshall, Lisa
    Born, Jan
    Martinetz, Thomas
    Claussen, Jens Christian
    [J]. PLOS COMPUTATIONAL BIOLOGY, 2016, 12 (09)
  • [10] The slow (&lt;1 Hz) rhythm of non-REM sleep: a dialogue between three cardinal oscillators
    Crunelli, Vincenzo
    Hughes, Stuart W.
    [J]. NATURE NEUROSCIENCE, 2010, 13 (01) : 10 - 18
12345