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Improved functional-weight approach to oscillatory patterns in excitable networks |
| Tao Li(李涛)1,2, Lin Yan(严霖)1,2, and Zhigang Zheng(郑志刚)1,2,3,† |
1 College of Information Science and Technology, Huaqiao University, Xiamen 361021, China;
2 Institute of Systems Science, Huaqiao University, Xiamen 361021, China;
3 School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China |
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Abstract Studies of sustained oscillations on complex networks with excitable node dynamics received much interest in recent years. Although an individual unit is non-oscillatory, they may organize to form various collective oscillatory patterns through networked connections. An excitable network usually possesses a number of oscillatory modes dominated by different Winfree loops and numerous spatiotemporal patterns organized by different propagation path distributions. The traditional approach of the so-called dominant phase-advanced drive method has been well applied to the study of stationary oscillation patterns on a network. In this paper, we develop the functional-weight approach that has been successfully used in studies of sustained oscillations in gene-regulated networks by an extension to the high-dimensional node dynamics. This approach can be well applied to the study of sustained oscillations in coupled excitable units. We tested this scheme for different networks, such as homogeneous random networks, small-world networks, and scale-free networks and found it can accurately dig out the oscillation source and the propagation path. The present approach is believed to have the potential in studies competitive non-stationary dynamics.
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Received: 18 April 2022
Revised: 11 May 2022
Accepted manuscript online: 29 May 2022
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PACS:
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05.45.Xt
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(Synchronization; coupled oscillators)
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87.19.lq
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(Neuronal wave propagation)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11875135). |
Corresponding Authors:
Zhigang Zheng
E-mail: zgzheng@hqu.edu.cn
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Cite this article:
Tao Li(李涛), Lin Yan(严霖), and Zhigang Zheng(郑志刚) Improved functional-weight approach to oscillatory patterns in excitable networks 2022 Chin. Phys. B 31 090502
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