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Optogenetic Entrainment of Hippocampal Theta Oscillations in Behaving Mice

Optogenetic Entrainment of Hippocampal Theta Oscillations in Behaving Mice

Published on: June 29, 2018

Delays and weakly coupled neuronal oscillators.

Bard Ermentrout¹, Tae-Wook Ko

¹Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA. bard@pitt.edu

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences

|February 17, 2009

Summary

Delays in neuronal oscillator systems can disrupt synchronization, leading to traveling waves. This study explores how constant and distributed delays affect coupled neuronal networks, revealing complex dynamics.

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Area of Science:

Computational neuroscience
Theoretical physics
Systems biology

Background:

Coupled oscillator systems are fundamental models for understanding neural network dynamics.
Time delays are inherent in biological systems, influencing signal transmission and network behavior.

Purpose of the Study:

To investigate the impact of constant and distributed time delays on the synchronization and dynamics of coupled neuronal oscillators.
To explore the emergence of traveling waves and loss of synchronization in networks with distance-dependent delays.

Main Methods:

Application of weakly coupled oscillator theory.
Utilizing mean-field theory for analyzing large networks with distributed delays.
Examination of phase models with stronger coupling and state-variable delays.

Main Results:

Constant delays in simple pairs can alter oscillatory patterns.
Distributed delays, particularly distance-dependent ones, can lead to traveling waves and desynchronization.
Stronger coupling and state-variable delays introduce richer dynamics, yet retain similarities to weakly coupled systems.

Conclusions:

Time delays are critical factors influencing the collective behavior of neuronal networks.
The nature of delays (constant vs. distributed) significantly impacts synchronization and network dynamics, potentially leading to complex emergent phenomena like traveling waves.