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Spiking neuron models with excitatory or inhibitory synaptic couplings and synchronization phenomena
Yasuomi D Sato1, Masatoshi Shiino
1Department of Applied Physics, Faculty of Science, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku, Tokyo 152-0033, Japan.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 22, 2002
Summary
This study explores how two model neurons synchronize using analytical and numerical methods. We identified conditions for in-phase and antiphase synchronized oscillations based on synaptic coupling and relaxation rates.
Area of Science:
- Computational Neuroscience
- Theoretical Neuroscience
- Mathematical Biology
Background:
- Neuronal synchronization is crucial for information processing in the brain.
- Understanding synchronization dynamics in neural networks is a key challenge in neuroscience.
Purpose of the Study:
- To analytically investigate synchronization phenomena in a system of two piecewise-linear model neurons.
- To determine the conditions governing in-phase and antiphase synchronized oscillations.
Main Methods:
- Phase plane analysis was employed to analyze the system dynamics.
- A singular perturbation approach was used to separate slow and fast dynamics.
- Analytical construction of the Poincaré map for piecewise-linear equations.
Main Results:
- Conditions for in-phase and antiphase synchronization were derived based on synaptic coupling strength and relaxation rate.
- Theoretical predictions were validated through numerical simulations.
- The study provides insights into the parameter space governing synchronized neuronal activity.
Conclusions:
- The study successfully characterized synchronization patterns in a simplified two-neuron model.
- Analytical methods provide a robust framework for understanding complex neural dynamics.
- Findings contribute to the theoretical understanding of neural network synchronization.