Sinusoidal disturbance induced topology identification of Hindmarsh-Rose neural networks

Topology identification of complex networks is an important problem. Existing research shows that the synchronization of network nodes is an obstacle in the identification of network topology. Identification of the structure of the network presents an interesting challenge during the synchronization of complex networks. We developed a new method using the sinusoidal disturbance to identify the topology when the complex network achieves synchronization. Compared with the disturbance of all the nodes, the disturbance of the key nodes alone can achieve a very good effect. Finally, numerical simulation data are provided to validate our hypothesis.概要中文概要拓扑识别是近年来复杂网络研究的重要问题, 研究表明, 网络上节点同步是拓扑识别过程中的重要障碍. 当节点到达同步时如何进行识别是一个非常有趣的问题. 本文主要研究了节点为Hindmarsh-Rose (HR) 系统的网络结构识别问题, 当网络上HR系统达到同步时, 它们不满足一致激励条件, 拓扑结构不能识别. 此时, 正弦信号扰动能够诱导拓扑识别. 相比于扰动网络上全部节点, 扰动关键节点也能达到拓扑识别的目的.创新点拓扑识别问题是复杂网络研究的重要问题, 研究结果表明, 当网络上的节点达到同步时候, 拓扑很难识别. 利用正弦扰动信号, 本文研究了当节点达到同步状态时的拓扑识别问题, 研究表明给节点添加适当的正弦扰动能够诱导出拓扑识别.

[1]  P. Olver.  Nonlinear Systems , 2013 .

[2]  J. Hindmarsh,et al.  A model of neuronal bursting using three coupled first order differential equations , 1984, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[3]  Chi Guo,et al.  Recovering network topologies via Taylor expansion and compressive sensing. , 2015, Chaos.

[4]  Zhong-Ping Jiang,et al.  Topology identification of complex dynamical networks. , 2010, Chaos.

[5]  Mingzhou Ding,et al.  Enhancement of neural synchrony by time delay. , 2004, Physical review letters.

[6]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[7]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[8]  Liang Chen,et al.  Synchronization: An Obstacle to Identification of Network Topology , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[9]  Xuerong Shi,et al.  Lag synchronization of multiple identical Hindmarsh–Rose neuron models coupled in a ring structure , 2010 .

[10]  Zengqiang Chen,et al.  Pinning weighted complex networks with heterogeneous delays by a small number of feedback controllers , 2008, Science in China Series F: Information Sciences.

[11]  T. Carroll,et al.  MASTER STABILITY FUNCTIONS FOR SYNCHRONIZED COUPLED SYSTEMS , 1999 .

[12]  Nathalie Corson,et al.  Modeling the Dynamics of Complex Interaction Systems: from Morphogenesis to Control , 2012, Int. J. Bifurc. Chaos.

[13]  Junan Lu,et al.  Pinning control of general complex dynamical networks with optimization , 2010, Science China Information Sciences.

[14]  Arkady Pikovsky,et al.  From complete to modulated synchrony in networks of identical Hindmarsh-Rose neurons , 2013, The European Physical Journal Special Topics.

[15]  Tianping Chen,et al.  Pinning Complex Networks by a Single Controller , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[16]  Bin Deng,et al.  Estimating and adjusting abnormal networks with unknown parameters and topology. , 2011, Chaos.

[17]  Martin Hasler,et al.  Generalized connection graph method for synchronization in asymmetrical networks , 2006 .

[18]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1990 .

[19]  Tianping Chen,et al.  Synchronization analysis of linearly coupled systems described by differential equations with a coupling delay , 2006 .

[20]  Suh-Yuh Yang,et al.  Effects of network structure on the synchronizability of nonlinearly coupled Hindmarsh-Rose neurons , 2015 .

[21]  S. Sastry,et al.  Adaptive Control: Stability, Convergence and Robustness , 1989 .

[22]  Junan Lu,et al.  Identifying Topologies of Complex Dynamical Networks With Stochastic Perturbations , 2016, IEEE Transactions on Control of Network Systems.

[23]  J. Hindmarsh,et al.  A model of the nerve impulse using two first-order differential equations , 1982, Nature.

[24]  Jinde Cao,et al.  Robust synchronization of coupled neural networks with mixed delays and uncertain parameters by intermittent pinning control , 2014, Neurocomputing.

[25]  G. Besançon.  Remarks on nonlinear adaptive observer design , 2000 .

[26]  Xiang Li,et al.  Pinning a complex dynamical network to its equilibrium , 2004, IEEE Trans. Circuits Syst. I Regul. Pap..

[27]  Wen-Xu Wang,et al.  Noise bridges dynamical correlation and topology in coupled oscillator networks. , 2010, Physical review letters.

[28]  Jinde Cao,et al.  Synchronization-based approach for parameters identification in delayed chaotic neural networks , 2007 .

[29]  Wenwu Yu,et al.  On pinning synchronization of complex dynamical networks , 2009, Autom..

[30]  M. Hasler,et al.  Connection Graph Stability Method for Synchronized Coupled Chaotic Systems , 2004 .

[31]  Junan Lu,et al.  Recovering Structures of Complex Dynamical Networks Based on Generalized Outer Synchronization , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[32]  Wei Xing Zheng,et al.  Inferring topologies of complex networks with hidden variables. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.