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Collective sustained oscillations in excitable small-world networks: the moderate fundamental loop or the minimum Winfree loop?

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Abstract

The problem of self-sustained oscillations in excitable complex networks is the central issue under investigation, among which the exploration of the key factors in determining collective oscillation and the realization of oscillation control are the challenging tasks. In this paper, we have extensively investigated the influence of the rewiring probability and the coupling strength on the oscillation period in excitable small-world networks (ESWNs) and exposed two determinants, i.e., the moderate fundamental loop (FL) and the minimum Winfree loop (MWL), which can effectively determine the oscillation period in ESWNs via different mechanisms. The moderate FL, which is created by the rewiring mechanism, can significantly influence the oscillation period in two ways. The first is to turn itself into the oscillation source, while the other is to behave as the competitor supervising the long oscillation source loop structure possessing the equivalent wavelength. The MWL, which is determined by the coupling strength, can profoundly affect the oscillation period by choosing the suitable FL to be the oscillation source at a given parameter setting. More importantly, corresponding to these two determinants, two control schemes that can effectively regulate the oscillation period in the ESWN have been proposed. We hope our results will shed light on a deeper understanding of the key factors in determining the oscillation period and the related period control in actual biological systems.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant Nos. 11675001 and 11875135), the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2019JM-045 and 2018JM6099), the Scientific Research Program Funded by Shaanxi Provincial Education Department (Program No. 19JK0039), Quanzhou City Science & Technology Program of China (No. 2018C085R), and the Scientific Research Funds of Huaqiao University (Grant No. 15BS401).

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Authors and Affiliations

  1. Nonlinear Research Institute, Baoji University of Arts and Sciences, Baoji, 721007, China

    Yu Qian, Chi Zhang, Gang Zhang & Fei Liu

  2. Advanced Titanium Alloys and Functional Coatings Cooperative Innovation Center, Baoji, 721007, China

    Yu Qian, Chi Zhang, Gang Zhang & Fei Liu

  3. Institute of Systems Science, Huaqiao University, Xiamen, 361021, China

    Zhigang Zheng

  4. College of Information Science and Engineering, Huaqiao University, Xiamen, 361021, China

    Zhigang Zheng

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  1. Yu Qian
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Qian, Y., Zhang, C., Zhang, G. et al. Collective sustained oscillations in excitable small-world networks: the moderate fundamental loop or the minimum Winfree loop?. Nonlinear Dyn 99, 1415–1431 (2020). https://doi.org/10.1007/s11071-019-05362-2

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