Attractive target wave patterns in complex networks consisting of excitable nodes

doi:10.1088/1674-1056/23/7/078906

中国物理B ›› 2014, Vol. 23 ›› Issue (7): 78906-078906.doi: 10.1088/1674-1056/23/7/078906

所属专题： TOPICAL REVIEW — Statistical Physics and Complex Systems

• TOPICAL REVIEW—Statistical Physics and Complex Systems • 上一篇下一篇

Attractive target wave patterns in complex networks consisting of excitable nodes

张立升^a, 廖旭红^b, 弭元元^{a c}, 钱郁^d, 胡岗^e

a State Key Laboratory of Cognitive Neuroscience and Learning, International Digital Group (IDG)/McGovern Institute for Brain Research,and Center for Collaboration and Innovation in Brain and Learning Sciences, Beijing Normal University, Beijing 100875, China;
b Center for Cognition and Brain Disorders, Hangzhou Normal University, Hangzhou 310036, China;
c Center for Systems Biology, Soochow University, Suzhou 215006, China;
d School of Physics and Information Technology, Baoji University of Arts and Sciences, Baoji 721013, China;
e Department of Physics, Beijing Normal University, Beijing 100875, China

收稿日期:2014-06-17 出版日期:2014-07-15 发布日期:2014-07-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11174034, 11135001, 11205041, and 11305112) and the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20130282).

Attractive target wave patterns in complex networks consisting of excitable nodes

Zhang Li-Sheng (张立升)^a, Liao Xu-Hong (廖旭红)^b, Mi Yuan-Yuan (弭元元)^{a c}, Qian Yu (钱郁)^d, Hu Gang (胡岗)^e

a State Key Laboratory of Cognitive Neuroscience and Learning, International Digital Group (IDG)/McGovern Institute for Brain Research,and Center for Collaboration and Innovation in Brain and Learning Sciences, Beijing Normal University, Beijing 100875, China;
b Center for Cognition and Brain Disorders, Hangzhou Normal University, Hangzhou 310036, China;
c Center for Systems Biology, Soochow University, Suzhou 215006, China;
d School of Physics and Information Technology, Baoji University of Arts and Sciences, Baoji 721013, China;
e Department of Physics, Beijing Normal University, Beijing 100875, China

Received:2014-06-17 Online:2014-07-15 Published:2014-07-15
Contact: Hu Gang E-mail:ganghu@bnu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11174034, 11135001, 11205041, and 11305112) and the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20130282).

摘要/Abstract

摘要： This review describes the investigations of oscillatory complex networks consisting of excitable nodes, focusing on the target wave patterns or say the target wave attractors. A method of dominant phase advanced driving (DPAD) is introduced to reveal the dynamic structures in the networks supporting oscillations, such as the oscillation sources and the main excitation propagation paths from the sources to the whole networks. The target center nodes and their drivers are regarded as the key nodes which can completely determine the corresponding target wave patterns. Therefore, the center (say node A) and its driver (say node B) of a target wave can be used as a label, (A,B), of the given target pattern. The label can give a clue to conveniently retrieve, suppress, and control the target waves. Statistical investigations, both theoretically from the label analysis and numerically from direct simulations of network dynamics, show that there exist huge numbers of target wave attractors in excitable complex networks if the system size is large, and all these attractors can be labeled and easily controlled based on the information given by the labels. The possible applications of the physical ideas and the mathematical methods about multiplicity and labelability of attractors to memory problems of neural networks are briefly discussed.

关键词: dominant phase advanced driving method, complex networks, labelable attractors, target wave patterns

Abstract: This review describes the investigations of oscillatory complex networks consisting of excitable nodes, focusing on the target wave patterns or say the target wave attractors. A method of dominant phase advanced driving (DPAD) is introduced to reveal the dynamic structures in the networks supporting oscillations, such as the oscillation sources and the main excitation propagation paths from the sources to the whole networks. The target center nodes and their drivers are regarded as the key nodes which can completely determine the corresponding target wave patterns. Therefore, the center (say node A) and its driver (say node B) of a target wave can be used as a label, (A,B), of the given target pattern. The label can give a clue to conveniently retrieve, suppress, and control the target waves. Statistical investigations, both theoretically from the label analysis and numerically from direct simulations of network dynamics, show that there exist huge numbers of target wave attractors in excitable complex networks if the system size is large, and all these attractors can be labeled and easily controlled based on the information given by the labels. The possible applications of the physical ideas and the mathematical methods about multiplicity and labelability of attractors to memory problems of neural networks are briefly discussed.

Key words: dominant phase advanced driving method, complex networks, labelable attractors, target wave patterns

中图分类号: (Structures and organization in complex systems)

89.75.Fb

89.75.Kd (Patterns) 05.65.+b (Self-organized systems)

张立升, 廖旭红, 弭元元, 钱郁, 胡岗. Attractive target wave patterns in complex networks consisting of excitable nodes[J]. 中国物理B, 2014, 23(7): 78906-078906.

Zhang Li-Sheng (张立升), Liao Xu-Hong (廖旭红), Mi Yuan-Yuan (弭元元), Qian Yu (钱郁), Hu Gang (胡岗). Attractive target wave patterns in complex networks consisting of excitable nodes[J]. Chin. Phys. B, 2014, 23(7): 78906-078906.

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Attractive target wave patterns in complex networks consisting of excitable nodes

Attractive target wave patterns in complex networks consisting of excitable nodes

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