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Automatic Detection of Highly Organized Theta Oscillations in the Murine EEG
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Detecting coexisting oscillatory patterns in delay coupled Lur'e systems.

Kirill Rogov1, Alexander Pogromsky1, Erik Steur1

  • 1Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven 5612 AZ, The Netherlands.

Chaos (Woodbury, N.Y.)
|April 3, 2021
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Summary
This summary is machine-generated.

This study introduces an efficient algorithm for analyzing complex oscillatory patterns in networks of delay-coupled Lur

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Area of Science:

  • Nonlinear Dynamics
  • Network Science
  • Control Theory

Background:

  • Delay-coupled identical Lur'e systems can exhibit complex dynamics.
  • Network equilibrium stability can change due to parameter variations in coupling.
  • Hopf bifurcations can lead to oscillatory patterns in these networks.

Purpose of the Study:

  • To develop a numerically efficient algorithm for computing oscillatory patterns in networks of delay-coupled Lur'e systems.
  • To analyze coexisting stable and unstable oscillatory patterns.
  • To gain deeper insight into network dynamics.

Main Methods:

  • Development of a numerically efficient algorithm for pattern computation.
  • Analysis of Hopf bifurcations (subcritical and supercritical).
  • Bifurcation analysis to explain coexisting modes.

Main Results:

  • A novel algorithm for computing oscillatory patterns in delay-coupled Lur'e systems is presented.
  • The algorithm successfully computes coexisting patterns, including both stable and unstable regimes.
  • Two examples illustrate the method's efficiency, involving subcritical and supercritical Hopf bifurcations.

Conclusions:

  • The proposed algorithm provides an efficient tool for analyzing complex dynamics in coupled nonlinear systems.
  • The ability to compute coexisting patterns offers significant insights into network behavior.
  • This work advances the understanding of pattern formation and stability in complex networks.