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The Study for Synchronization between Two Coupled FitzHugh-Nagumo Neurons Based on the Laplace Transform and the
1School of Environment and Architecture, University of Shanghai for Science and Technology, Shanghai 200093, China.
Neural Plasticity
|May 13, 2021
Summary
Synchronization in coupled FitzHugh-Nagumo (FHN) neurons depends solely on coupling strength, not external current. Analytical methods reveal conditions for synchronization, achieving rest states or spikes based on current presence.
Area of Science:
- Computational Neuroscience
- Nonlinear Dynamics
- Mathematical Biology
Background:
- The FitzHugh-Nagumo (FHN) model is a simplified mathematical model of excitable systems, commonly used to study neuronal behavior.
- Neuronal synchronization is crucial for information processing in the brain, and understanding its mechanisms is a key research area.
Purpose of the Study:
- To analytically investigate the synchronization dynamics of two coupled FitzHugh-Nagumo neurons.
- To determine the conditions under which synchronization occurs, considering the influence of external current.
Main Methods:
- Utilized the Laplace transform and the Adomian decomposition method for analytical solutions.
- Expressed the synchronization error system as Volterra integral equations.
- Employed successive approximation methods for integral equations and verified results with numerical simulations.
Main Results:
- Synchronization conditions were analytically derived and confirmed numerically.
- The occurrence of synchronization was found to depend exclusively on coupling strength, independent of external current.
- Synchronous rest states were achieved without external current, while synchronous spikes emerged with non-zero external current.
Conclusions:
- The study provides a novel analytical framework for understanding neuronal synchronization using integral equations.
- Coupling strength is the sole determinant for synchronization in the studied FHN neuron model.
- The nature of synchronization (rest state vs. spikes) is modulated by the presence of external current.
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