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Complete synchronization of three-layer Rulkov neuron network coupled by electrical and chemical synapses
Penghe Ge1, Libo Cheng2, Hongjun Cao3
1Department of Mathematics, School of Mathematics and Statistics, Changchun University of Science and Technology, Changchun 130022, People's Republic of China.
Chaos (Woodbury, N.Y.)
|April 8, 2024
Summary
This study explores complete synchronization in a three-layer Rulkov neuron network. Periodic synchronization manifolds enable full synchronization, unlike chaotic ones, revealing network dynamics.
Area of Science:
- Computational Neuroscience
- Complex Systems
Background:
- Neuronal network models are crucial for understanding brain function.
- Electrical and chemical synapses play distinct roles in neural communication.
- Complete synchronization in complex networks is a key phenomenon.
Purpose of the Study:
- To analyze complete synchronization in a three-layer Rulkov neuron network with mixed coupling.
- To develop and apply the master stability function method for non-Laplacian networks.
- To investigate the conditions and dynamics of synchronization manifolds.
Main Methods:
- Master stability function (MSF) method adapted for non-Laplacian coupling.
- Analysis of invariant manifold dynamics for synchronization.
- Lyapunov exponent calculations to determine synchronization stability.
- Simulation of network behavior under perturbations.
Main Results:
- Existence conditions for synchronization manifolds with nonlinear chemical coupling were established.
- Transient chaotic and periodic windows were observed before asymptotic behavior.
- Periodic synchronization manifolds lead to complete synchronization; chaotic ones do not.
- Network dynamics under small perturbations were simulated.
Conclusions:
- Complete synchronization is achievable in this Rulkov neuron network model under specific conditions.
- The MSF method is effective for analyzing synchronization in networks with non-Laplacian coupling.
- The nature of the synchronization manifold (periodic vs. chaotic) dictates synchronization outcomes.
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