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Minimum Winfree loop determines self-sustained oscillations in excitable Erdös-Rényi random networks
Yu Qian1, Xiaohua Cui2, Zhigang Zheng3,4
1Nonlinear Research Institute, Baoji University of Arts and Sciences, Baoji, 721007, China. qianyu0272@163.com.
Scientific Reports
|July 20, 2017
Summary
The minimum Winfree loop (MWL) is the key factor for collective oscillations in excitable random networks. Network structure analysis can predict critical connection probabilities, aiding understanding of biological system activity.
Area of Science:
- Complex networks
- Neuroscience
- Computational biology
Background:
- Understanding self-sustained oscillations in excitable complex networks is crucial for brain system activity.
- Identifying key determinants of these oscillations remains a significant challenge in the field.
Purpose of the Study:
- To investigate the influence of system parameters on self-sustained oscillations in excitable Erdös-Rényi random networks (EERRNs).
- To identify the primary factor determining the emergence of collective oscillations in these networks.
Main Methods:
- Analysis of system parameters influencing self-sustained oscillations in EERRNs.
- Investigation of the relationship between network structure and oscillation emergence.
- Numerical simulations to verify theoretical predictions.
Main Results:
- The minimum Winfree loop (MWL) was identified as the key determinant for collective oscillations.
- A one-to-one correspondence was established between optimal connection probability (OCP) and MWL length.
- Lower critical connection probability (LCCP), OCP, and upper critical connection probability (UCCP) are determined by MWL and predictable via network structure analysis.
Conclusions:
- The MWL is a critical network property governing collective oscillations in excitable random networks.
- Network structure analysis provides a method for predicting key parameters related to oscillation emergence.
- These findings offer insights into the determinants of persistent activity in biological systems.
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