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Stochastic bursting in unidirectionally delay-coupled noisy excitable systems
Chunming Zheng1, Arkady Pikovsky1
1Institute for Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Strasse 24/25, 14476 Potsdam-Golm, Germany.
Chaos (Woodbury, N.Y.)
|May 3, 2019
Summary
Stochastic bursting in noisy excitable systems arises from time-delayed coupling and noise. This phenomenon, observed in networks, exhibits a leader-follower dynamic, explained by a coupled point process model.
Area of Science:
- Computational Neuroscience
- Complex Systems
- Nonlinear Dynamics
Background:
- Noisy excitable systems are fundamental to understanding biological and artificial neural networks.
- Time-delayed coupling is a common feature in neural systems, influencing network dynamics.
- Stochastic phenomena play a crucial role in information processing in the brain.
Purpose of the Study:
- To investigate the emergence of stochastic bursting in unidirectional delay-coupled noisy excitable systems.
- To analyze the impact of time-delayed coupling and noise on network coherence.
- To develop an analytical framework for describing the observed spike patterns.
Main Methods:
- Simulations of a ring network of unidirectional delay-coupled noisy excitable systems (theta-neurons).
- Application of timescale separation approximation for analytical modeling.
- Derivation of spike statistics, pairwise correlations, and network output spectrum.
Main Results:
- Stochastic bursting is observed and attributed to the interplay of time-delayed coupling and noise.
- A leader-follower relationship emerges in the coherent spike patterns under timescale separation.
- Analytical derivations for spike statistics and correlations show good agreement with simulation results.
Conclusions:
- Time-delayed coupling and noise are key drivers of stochastic bursting in these systems.
- The leader-follower dynamics can be effectively modeled using a coupled point process.
- The theoretical framework provides accurate predictions for network behavior, validated by theta-neuron simulations.
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