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Neuronal oscillations and stochastic limit cycles

C Kurrer¹, K Schulten

¹Department of Physics and Beckman Institute, University of Illinois at Urbana-Champaign 61801, USA. kurrer@ton.scphys.kyoto-u.ac.jp

International Journal of Neural Systems

|September 1, 1996

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This study reveals two novel phase transitions in coupled excitable neural networks, impacting synchronous firing behavior. These findings offer new insights into neural synchronization dynamics.

Area of Science:

Computational neuroscience
Nonlinear dynamics
Complex systems

Background:

Neural networks exhibit complex dynamics, including excitable and oscillatory behaviors.
Understanding synchronization is crucial for deciphering neural communication.

Purpose of the Study:

To investigate phase transitions in synchronous activity within networks of coupled neurons.
To analyze the distinct synchronization behaviors of excitable versus oscillatory systems.

Main Methods:

Development and analysis of a mathematical model for coupled neurons.
Employing analytical calculations and computer simulations.
Utilizing the concept of Stochastic Limit Cycles for derivation.

Main Results:

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Identified two distinct phase transitions from synchronous to asynchronous firing.
One transition resembles known oscillator synchronization; the second is unique to excitable systems.
Provided an analytical derivation of these transitions.

Conclusions:

Coupled excitable systems exhibit unique synchronization phenomena beyond those in oscillators.
The findings advance the understanding of phase transitions in biological neural networks.
Highlights the importance of considering neuronal excitability in network dynamics.