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題名 具非線性連接之Hindmarsh-Rose神經元耦合系統的同步化研究
Synchronization of nonlinearly coupled systems of Hindmarsh-Rose neurons with time delays作者 陳柏艾
Chen, Bo-Ai貢獻者 曾睿彬
Tseng, Jui-Pin
陳柏艾
Chen, Bo-Ai關鍵詞 連接系統
同步化
延遲
非線性連接
Hindmarsh-Rose神經元
Coupled system
Synchronization
Delay
Nonlinear coupling
Hindmarsh-Rose neuron日期 2020 上傳時間 5-Feb-2020 17:59:32 (UTC+8) 摘要 在此論文,我們研究Hindmarsh-Rose 神經元耦合系統的同步化,我們所考慮的模型之耦合結構可以相等的一般性。模型所具備的耦合函數可以是非線性的,耦合矩陣可容許非零的非對角元素能有不同的正負號,並且我們也考慮耦合時間延遲。藉由[33] 的同步化理論,我們推導出與時間延遲相關的同步化條件。我們提供兩個數值例子來表現本論文同步化理論之效用。
In this thesis, we investigate the synchronization of coupled systems of Hindmarsh-Rose neurons. The coupling scheme under consideration is general. The coupling functions could be non-linear. The connection matrix could have non-zero and non-diagonal entries with different signs. We also consider the transmission delays in the coupling terms of the coupled systems. We derive a delay-dependent criterion that leads to the synchronization of coupled neurons. Twoexamples with numerical simulations are illustrated to show the effectiveness of theoretical result.參考文獻 [1] Editors. Communications in Nonlinear Science and Numerical Simulation, 13(9): IFC, 2008.[2] Igor Belykh, Enno de Lange, and Martin Hasler. Synchronization of bursting neurons: What matters in the network topology. Phys. Rev. Lett., 94:188101, May 2005.[3] R. Bharath and Massachusetts Institute of Technology. Department of Mechanical Engineering. Nonlinear Observer Design and Synchronization Analysis for Classical Models of Neural Oscillators. Massachusetts Institute of Technology, Department of Mechanical Engineering, 2013.[4] Ranjeetha Bharath and Jean-Jacques Slotine. Nonlinear observer design and synchronization analysis for classical models of neural oscillators. 2013.[5] S. M. Crook, G. B. Ermentrout, M. C. Vanier, and J. M. Bower. The role of axonal delay in the synchronization of networks of coupled cortical oscillators. Journal of Computational Neuroscience, 4(2):161–172, 1997.[6] Marshall Crumiller, Bruce Knight, Yunguo Yu, and Ehud Kaplan. Estimating the amount of information conveyed by a population of neurons. Front Neurosci, 5:90, 2011.[7] Enno de Lange and Martin Hasler. Predicting single spikes and spike patterns with the hindmarsh–rose model. Biological Cybernetics, 99(4):349, 2008.[8] Mukeshwar Dhamala, Viktor K. Jirsa, and Mingzhou Ding. Transitions to synchrony in coupled bursting neurons. Phys. Rev. Lett., 92:028101, Jan 2004.[9] Ruijin Du, Lixin Tian, Gaogao Dong, Yi Huang, Jun Xia Ruijin Du, Lixin Tian, Gaogao Dong, Yi Huang, and Jun Xia. Synchronization analysis for nonlinearly coupled complex networks of non-delayed and delayed coupling with asymmetrical coupling matrices. 2013.[10] J. L. Hindmarsh, R. M. Rose, and Andrew Fielding Huxley. A model of neuronal bursting using three coupled first order differential equations. Proceedings of the Royal Society of London. Series B. Biological Sciences, 221(1222):87–102, 1984.[11] G. Innocenti and R. Genesio. On the dynamics of chaotic spiking-bursting transition in the hindmarsh–rose neuron. Chaos: An Interdisciplinary Journal of Nonlinear Science, 19(2):023124, 2009.[12] Viktor K. Jirsa and Viktor K. Jirsa A.R. McIntosh, editors. Handbook of Brain Connectivity. Number X, 528 in Understanding Complex Systems. Springer-Verlag Berlin Heidelberg, 1 edition, 2007.[13] James Keener and James Sneyd. Mathematical Physiology. Springer-Verlag, Berlin, Heidelberg, 1998.[14] Ron Levy, William D. Hutchison, Andres M. Lozano, and Jonathan O. Dostrovsky. High-frequency synchronization of neuronal activity in the subthalamic nucleus of parkinsonian patients with limb tremor. The Journal of Neuroscience, 20(20):7766–7775, October 2000.[15] Simon J. G. Lewis and Roger A. Barker. Understanding the dopaminergic deficits in parkinson’s disease: Insights into disease heterogeneity. Journal of Clinical Neuroscience, 16(5):620–625, 2019/12/11 2009.[16] Chun-Hsien Li and Suh-Yuh Yang. A graph approach to synchronization in complex networks of asymmetrically nonlinear coupled dynamical systems. Journal of the London Mathematical Society, 83(3):711–732, 03 2011.[17] Chun-Hsien Li and Suh-Yuh Yang. Eventual dissipativeness and synchronization of nonlinearly coupled dynamical network of hindmarsh–rose neurons. Applied Mathematical Modelling, 39(21):6631 – 6644, 2015.[18] Xiwei Liu and Tianping Chen. Exponential synchronization of nonlinear coupled dynamical networks with a delayed coupling. Physica A: Statistical Mechanics and its Applications, 381:82 – 92, 2007.[19] Xiwei Liu and Tianping Chen. Exponential synchronization of nonlinear coupled dynamical networks with a delayed coupling. Physica A: Statistical Mechanics and its Applications, 381(C):82–92, 2007.[20] Xiwei Liu and Tianping Chen. Synchronization analysis for nonlinearly-coupled complex networks with an asymmetrical coupling matrix. Physica A: Statistical Mechanics and its Applications, 387(16):4429 – 4439, 2008.[21] Arefeh Mazarei, Mohammad Matlob, Gholamhossein Riazi, and Yousef Jamali. The role of topology in the synchronization of neuronal networks based on the hodgkin-huxley model. 12 2018.[22] Georgi S. Medvedev and Nancy Kopell. Synchronization and transient dynamics in the chains of electrically coupled fitzhugh-nagumo oscillators. SIAM Journal on Applied Mathematics, 61(5):1762–1801, 2001.[23] Renato E. Mirollo and Steven H. Strogatz. Synchronization of pulse-coupled biological oscillators. SIAM Journal on Applied Mathematics, 50(6):1645–1662, 1990.[24] Florian Mormann, Thomas Kreuz, Ralph G Andrzejak, Peter David, Klaus Lehnertz, and Christian E Elger. Epileptic seizures are preceded by a decrease in synchronization. Epilepsy Research, 53(3):173 – 185, 2003.[25] Ernst Niebur, Steven S Hsiao, and Kenneth O Johnson. Synchrony: a neuronal mechanism for attentional selection? Current Opinion in Neurobiology, 12(2):190 – 194, 2002.[26] George Parish, Simon Hanslmayr, and Howard Bowman. The sync/desync model: How a synchronized hippocampus and a desynchronized neocortex code memories. Journal ofNeuroscience, 38(14):3428–3440, 2018.[27] LOUIS M. PECORA and THOMAS L. CARROLL. Master stability functions for synchronized coupled systems. International Journal of Bifurcation and Chaos, 09(12): 2315–2320, 1999.[28] T. de L. Prado, S. R. Lopes, C. A. S. Batista, J. Kurths, and R. L. Viana. Synchronization of bursting hodgkin-huxley-type neurons in clustered networks. Phys. Rev. E, 90:032818, Sep 2014.[29] Chih-Wen. Shih and Jui-Pin. Tseng. A general approach to synchronization of coupled cells. SIAM Journal on Applied Dynamical Systems, 12(3):1354–1393, 2013.[30] Qiankun Song. Synchronization analysis in an array of asymmetric neural networks with time-varying delays and nonlinear coupling. Applied Mathematics and Computation, 216(5):1605 – 1613, 2010.[31] Steven Strogatz and Ian Stewart. Coupled oscillators and biological synchronization. Scientific American, 269:102–9, 01 1994.[32] Raúl Toral, C Masoller, Claudio R Mirasso, M Ciszak, and O Calvo. Characterization of the anticipated synchronization regime in the coupled fitzhugh–nagumo model for neurons. Physica A: Statistical Mechanics and its Applications, 325(1):192 – 198, 2003. StochasticSystems: From Randomness to Complexity.[33] Jui-Pin Tseng. A novel approach to synchronization of nonlinearly coupled network systems with delays. Physica A: Statistical Mechanics and its Applications, 452:266 – 280, 2016.[34] Ahmet Uçar, Karl E. Lonngren, and Er-Wei Bai. Synchronization of the coupled fitzhugh–nagumo systems. Chaos, Solitons & Fractals, 20(5):1085 – 1090, 2004.[35] Kaijun Wu, Tiejun Wang, Chunli Wang, Tiaotiao Du, and Huaiwei Lu. Study on electrical synapse coupling synchronization of hindmarsh-rose neurons under gaussian white noise.Neural Computing and Applications, 30(2):551–561, nov 2016.[36] Kaijun Wu, Boping Zhang, Bin Tian, Sanshan Du, and Huaiwei Lu. Synchronization study of hindmarsh—rose neuron coupled system based on numerical simulation of time delay. Cluster Computing, 20(4):3287–3297, December 2017.[37] Shi Xia and Lu Qi-Shao. Complete synchronization of coupled hindmarsh–rose neurons with ring structure. Chinese Physics Letters, 21(9):1695–1698, aug 2004.[38] Shi Xia and Lu Qi-Shao. Firing patterns and complete synchronization of coupled hindmarsh–rose neurons. Chinese Physics, 14(1):77–85, dec 2004.[39] T. Yang, Z. Meng, G. Shi, Y. Hong, and K. H. Johansson. Network synchronization with nonlinear dynamics and switching interactions. IEEE Transactions on Automatic Control, 61(10):3103–3108, October 2016. 描述 碩士
國立政治大學
應用數學系
105751008資料來源 http://thesis.lib.nccu.edu.tw/record/#G0105751008 資料類型 thesis dc.contributor.advisor 曾睿彬 zh_TW dc.contributor.advisor Tseng, Jui-Pin en_US dc.contributor.author (Authors) 陳柏艾 zh_TW dc.contributor.author (Authors) Chen, Bo-Ai en_US dc.creator (作者) 陳柏艾 zh_TW dc.creator (作者) Chen, Bo-Ai en_US dc.date (日期) 2020 en_US dc.date.accessioned 5-Feb-2020 17:59:32 (UTC+8) - dc.date.available 5-Feb-2020 17:59:32 (UTC+8) - dc.date.issued (上傳時間) 5-Feb-2020 17:59:32 (UTC+8) - dc.identifier (Other Identifiers) G0105751008 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/128609 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 應用數學系 zh_TW dc.description (描述) 105751008 zh_TW dc.description.abstract (摘要) 在此論文,我們研究Hindmarsh-Rose 神經元耦合系統的同步化,我們所考慮的模型之耦合結構可以相等的一般性。模型所具備的耦合函數可以是非線性的,耦合矩陣可容許非零的非對角元素能有不同的正負號,並且我們也考慮耦合時間延遲。藉由[33] 的同步化理論,我們推導出與時間延遲相關的同步化條件。我們提供兩個數值例子來表現本論文同步化理論之效用。 zh_TW dc.description.abstract (摘要) In this thesis, we investigate the synchronization of coupled systems of Hindmarsh-Rose neurons. The coupling scheme under consideration is general. The coupling functions could be non-linear. The connection matrix could have non-zero and non-diagonal entries with different signs. We also consider the transmission delays in the coupling terms of the coupled systems. We derive a delay-dependent criterion that leads to the synchronization of coupled neurons. Twoexamples with numerical simulations are illustrated to show the effectiveness of theoretical result. en_US dc.description.tableofcontents Chapter1 Introduction 1Chapter2 Preliminaries 4Chapter3 Synchronization of Hindmarsh-Rose neurons 11Chapter4 Numerical examples 20Chapter5 Conclusion 32Bibliography 33 zh_TW dc.format.extent 1802327 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0105751008 en_US dc.subject (關鍵詞) 連接系統 zh_TW dc.subject (關鍵詞) 同步化 zh_TW dc.subject (關鍵詞) 延遲 zh_TW dc.subject (關鍵詞) 非線性連接 zh_TW dc.subject (關鍵詞) Hindmarsh-Rose神經元 zh_TW dc.subject (關鍵詞) Coupled system en_US dc.subject (關鍵詞) Synchronization en_US dc.subject (關鍵詞) Delay en_US dc.subject (關鍵詞) Nonlinear coupling en_US dc.subject (關鍵詞) Hindmarsh-Rose neuron en_US dc.title (題名) 具非線性連接之Hindmarsh-Rose神經元耦合系統的同步化研究 zh_TW dc.title (題名) Synchronization of nonlinearly coupled systems of Hindmarsh-Rose neurons with time delays en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) [1] Editors. Communications in Nonlinear Science and Numerical Simulation, 13(9): IFC, 2008.[2] Igor Belykh, Enno de Lange, and Martin Hasler. Synchronization of bursting neurons: What matters in the network topology. Phys. Rev. Lett., 94:188101, May 2005.[3] R. Bharath and Massachusetts Institute of Technology. Department of Mechanical Engineering. Nonlinear Observer Design and Synchronization Analysis for Classical Models of Neural Oscillators. Massachusetts Institute of Technology, Department of Mechanical Engineering, 2013.[4] Ranjeetha Bharath and Jean-Jacques Slotine. Nonlinear observer design and synchronization analysis for classical models of neural oscillators. 2013.[5] S. M. Crook, G. B. Ermentrout, M. C. Vanier, and J. M. Bower. The role of axonal delay in the synchronization of networks of coupled cortical oscillators. Journal of Computational Neuroscience, 4(2):161–172, 1997.[6] Marshall Crumiller, Bruce Knight, Yunguo Yu, and Ehud Kaplan. Estimating the amount of information conveyed by a population of neurons. Front Neurosci, 5:90, 2011.[7] Enno de Lange and Martin Hasler. Predicting single spikes and spike patterns with the hindmarsh–rose model. Biological Cybernetics, 99(4):349, 2008.[8] Mukeshwar Dhamala, Viktor K. Jirsa, and Mingzhou Ding. Transitions to synchrony in coupled bursting neurons. Phys. Rev. Lett., 92:028101, Jan 2004.[9] Ruijin Du, Lixin Tian, Gaogao Dong, Yi Huang, Jun Xia Ruijin Du, Lixin Tian, Gaogao Dong, Yi Huang, and Jun Xia. Synchronization analysis for nonlinearly coupled complex networks of non-delayed and delayed coupling with asymmetrical coupling matrices. 2013.[10] J. L. Hindmarsh, R. M. Rose, and Andrew Fielding Huxley. A model of neuronal bursting using three coupled first order differential equations. Proceedings of the Royal Society of London. Series B. Biological Sciences, 221(1222):87–102, 1984.[11] G. Innocenti and R. Genesio. On the dynamics of chaotic spiking-bursting transition in the hindmarsh–rose neuron. Chaos: An Interdisciplinary Journal of Nonlinear Science, 19(2):023124, 2009.[12] Viktor K. Jirsa and Viktor K. Jirsa A.R. McIntosh, editors. Handbook of Brain Connectivity. Number X, 528 in Understanding Complex Systems. Springer-Verlag Berlin Heidelberg, 1 edition, 2007.[13] James Keener and James Sneyd. Mathematical Physiology. Springer-Verlag, Berlin, Heidelberg, 1998.[14] Ron Levy, William D. Hutchison, Andres M. Lozano, and Jonathan O. Dostrovsky. High-frequency synchronization of neuronal activity in the subthalamic nucleus of parkinsonian patients with limb tremor. The Journal of Neuroscience, 20(20):7766–7775, October 2000.[15] Simon J. G. Lewis and Roger A. Barker. Understanding the dopaminergic deficits in parkinson’s disease: Insights into disease heterogeneity. Journal of Clinical Neuroscience, 16(5):620–625, 2019/12/11 2009.[16] Chun-Hsien Li and Suh-Yuh Yang. A graph approach to synchronization in complex networks of asymmetrically nonlinear coupled dynamical systems. Journal of the London Mathematical Society, 83(3):711–732, 03 2011.[17] Chun-Hsien Li and Suh-Yuh Yang. Eventual dissipativeness and synchronization of nonlinearly coupled dynamical network of hindmarsh–rose neurons. Applied Mathematical Modelling, 39(21):6631 – 6644, 2015.[18] Xiwei Liu and Tianping Chen. Exponential synchronization of nonlinear coupled dynamical networks with a delayed coupling. Physica A: Statistical Mechanics and its Applications, 381:82 – 92, 2007.[19] Xiwei Liu and Tianping Chen. Exponential synchronization of nonlinear coupled dynamical networks with a delayed coupling. Physica A: Statistical Mechanics and its Applications, 381(C):82–92, 2007.[20] Xiwei Liu and Tianping Chen. Synchronization analysis for nonlinearly-coupled complex networks with an asymmetrical coupling matrix. Physica A: Statistical Mechanics and its Applications, 387(16):4429 – 4439, 2008.[21] Arefeh Mazarei, Mohammad Matlob, Gholamhossein Riazi, and Yousef Jamali. The role of topology in the synchronization of neuronal networks based on the hodgkin-huxley model. 12 2018.[22] Georgi S. Medvedev and Nancy Kopell. Synchronization and transient dynamics in the chains of electrically coupled fitzhugh-nagumo oscillators. SIAM Journal on Applied Mathematics, 61(5):1762–1801, 2001.[23] Renato E. Mirollo and Steven H. Strogatz. Synchronization of pulse-coupled biological oscillators. SIAM Journal on Applied Mathematics, 50(6):1645–1662, 1990.[24] Florian Mormann, Thomas Kreuz, Ralph G Andrzejak, Peter David, Klaus Lehnertz, and Christian E Elger. Epileptic seizures are preceded by a decrease in synchronization. Epilepsy Research, 53(3):173 – 185, 2003.[25] Ernst Niebur, Steven S Hsiao, and Kenneth O Johnson. Synchrony: a neuronal mechanism for attentional selection? Current Opinion in Neurobiology, 12(2):190 – 194, 2002.[26] George Parish, Simon Hanslmayr, and Howard Bowman. The sync/desync model: How a synchronized hippocampus and a desynchronized neocortex code memories. Journal ofNeuroscience, 38(14):3428–3440, 2018.[27] LOUIS M. PECORA and THOMAS L. CARROLL. Master stability functions for synchronized coupled systems. International Journal of Bifurcation and Chaos, 09(12): 2315–2320, 1999.[28] T. de L. Prado, S. R. Lopes, C. A. S. Batista, J. Kurths, and R. L. Viana. Synchronization of bursting hodgkin-huxley-type neurons in clustered networks. Phys. Rev. E, 90:032818, Sep 2014.[29] Chih-Wen. Shih and Jui-Pin. Tseng. A general approach to synchronization of coupled cells. SIAM Journal on Applied Dynamical Systems, 12(3):1354–1393, 2013.[30] Qiankun Song. Synchronization analysis in an array of asymmetric neural networks with time-varying delays and nonlinear coupling. Applied Mathematics and Computation, 216(5):1605 – 1613, 2010.[31] Steven Strogatz and Ian Stewart. Coupled oscillators and biological synchronization. Scientific American, 269:102–9, 01 1994.[32] Raúl Toral, C Masoller, Claudio R Mirasso, M Ciszak, and O Calvo. Characterization of the anticipated synchronization regime in the coupled fitzhugh–nagumo model for neurons. Physica A: Statistical Mechanics and its Applications, 325(1):192 – 198, 2003. StochasticSystems: From Randomness to Complexity.[33] Jui-Pin Tseng. A novel approach to synchronization of nonlinearly coupled network systems with delays. Physica A: Statistical Mechanics and its Applications, 452:266 – 280, 2016.[34] Ahmet Uçar, Karl E. Lonngren, and Er-Wei Bai. Synchronization of the coupled fitzhugh–nagumo systems. Chaos, Solitons & Fractals, 20(5):1085 – 1090, 2004.[35] Kaijun Wu, Tiejun Wang, Chunli Wang, Tiaotiao Du, and Huaiwei Lu. Study on electrical synapse coupling synchronization of hindmarsh-rose neurons under gaussian white noise.Neural Computing and Applications, 30(2):551–561, nov 2016.[36] Kaijun Wu, Boping Zhang, Bin Tian, Sanshan Du, and Huaiwei Lu. Synchronization study of hindmarsh—rose neuron coupled system based on numerical simulation of time delay. Cluster Computing, 20(4):3287–3297, December 2017.[37] Shi Xia and Lu Qi-Shao. Complete synchronization of coupled hindmarsh–rose neurons with ring structure. Chinese Physics Letters, 21(9):1695–1698, aug 2004.[38] Shi Xia and Lu Qi-Shao. Firing patterns and complete synchronization of coupled hindmarsh–rose neurons. Chinese Physics, 14(1):77–85, dec 2004.[39] T. Yang, Z. Meng, G. Shi, Y. Hong, and K. H. Johansson. Network synchronization with nonlinear dynamics and switching interactions. IEEE Transactions on Automatic Control, 61(10):3103–3108, October 2016. zh_TW dc.identifier.doi (DOI) 10.6814/NCCU202000086 en_US