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Related Experiment Video

Updated: Dec 26, 2025

Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients

Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients

Published on: December 18, 2016

Echo in complex networks.

Richa Phogat¹, Sudeshna Sinha^1,2, P Parmananda¹

¹Department of Physics, Indian Institute of Technology, Bombay, Powai, Mumbai 400 076, India.

Physical Review. E

|March 15, 2020

Summary

This summary is machine-generated.

Network topology significantly influences oscillator echo behavior. Randomizing connections can induce echoes in low-average-degree networks, while dynamic links disrupt echoes in sparse networks but preserve them in dense ones.

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Microstate and Omega Complexity Analyses of the Resting-state Electroencephalography

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Published on: June 15, 2018

Area of Science:

Complex systems
Nonlinear dynamics
Network science

Background:

Globally coupled oscillators can exhibit echo behavior, a spontaneous increase in order parameter following two perturbations.
This phenomenon has been observed in various oscillatory systems.

Purpose of the Study:

To investigate the impact of network topology on the emergence and characteristics of echo behavior in coupled oscillators.
To explore the roles of average degree and network randomness in echo formation.

Main Methods:

Utilized the Watts-Strogatz algorithm to generate small-world networks, ranging from regular rings to random networks.
Systematically varied the average degree and rewiring probability to control network topology.
Analyzed the presence and size of echoes under different network configurations and dynamic link conditions.

Main Results:

Echoes are not observed in regular rings with low average degrees and high coupling.
Sufficient randomness in connections can reintroduce echoes in sparse networks.
Increasing average degree in regular networks above a critical value leads to echo emergence.
Random networks exhibit echoes across all average degrees.
Intermediate randomness shows a nonmonotonic dependence of echo size on average degree, with a minimum at intermediate values.
Dynamically changing links abolish echoes in low-average-degree networks but preserve them in high-average-degree networks.

Conclusions:

Network topology is a critical determinant of echo behavior in coupled oscillators.
Randomizing network connections is a viable strategy to induce echoes, especially in sparse systems.
Dynamic links can either destroy or preserve echoes depending on the network's average degree, highlighting the importance of network structure for echo robustness.