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A Synchronization Criterion for Two Hindmarsh-Rose Neurons with Linear and Nonlinear Coupling Functions Based on the
Chunlin Su1, Bin Zhen1, Zigen Song2
1School of Environment and Architecture, University of Shanghai for Science and Technology, Shanghai 200093, China.
Neural Plasticity
|February 19, 2021
Summary
This study proposes an analytical criterion for Hindmarsh-Rose (HR) neuron synchronization using Laplace transforms. The method accurately predicts synchronization for various behaviors and is computationally efficient for large networks.
Area of Science:
- Computational Neuroscience
- Nonlinear Dynamics
- Systems Biology
Background:
- Hindmarsh-Rose (HR) neurons exhibit complex dynamics, including periodic and chaotic firing patterns.
- Understanding synchronization in coupled neuronal networks is crucial for deciphering brain function.
- Previous synchronization analyses often involve complex numerical methods or limitations in coupling types.
Purpose of the Study:
- To develop a novel analytical criterion for investigating synchronization between two linearly and nonlinearly coupled HR neurons.
- To provide a more convenient method for analyzing synchronization by reformulating the error system in integral form.
- To establish a computationally efficient approach applicable to large-scale neuronal networks.
Main Methods:
- Utilizing the Laplace transform method to analyze the synchronization error system.
- Converting the synchronization problem into a root stability analysis of a nonlinear algebraic equation.
- Applying the Routh-Hurwitz criterion to derive the analytical synchronization criterion.
Main Results:
- An analytical criterion for HR neuron synchronization was successfully derived.
- The criterion is validated through numerical simulations for both periodic and chaotic HR neuron behaviors.
- The derived analytical results demonstrate high accuracy, comparable to the conditional Lyapunov method.
- The method requires small computational resources, facilitating scalability to larger neuron populations.
Conclusions:
- The proposed analytical criterion offers a robust and efficient method for assessing synchronization in coupled HR neurons.
- The integral form of the synchronization error system simplifies analysis and enhances applicability.
- This approach is readily extendable for studying synchronization in large networks of HR neurons.
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