Synchronization in phase-coupled Kuramoto oscillator networks with axonal delay and synaptic plasticity
1Department of Physics and Astronomy, Dickinson College, Carlisle, Pennsylvania 17013, USA.
Summary
We studied coupled phase oscillators with time delay and Hebbian learning. Combining these effects leads to novel synchronization phenomena and spatiotemporal patterns in oscillator networks.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Computational neuroscience
Background:
- The Kuramoto model describes synchronization in coupled oscillators.
- Neuroscience principles like Hebbian learning and finite signal speeds are crucial for biological networks.
- Understanding emergent behaviors in coupled systems is a key challenge.
Purpose of the Study:
- To investigate synchronization phenomena in coupled phase oscillators.
- To analyze the combined effects of time delay and Hebbian-inspired network plasticity.
- To explore pattern formation in one- and two-dimensional oscillator lattices.
Main Methods:
- Analytical and numerical exploration of a Kuramoto-type system.
- Incorporation of time-delayed coupling.
- Modeling dynamic coupling constants based on the Hebbian learning rule.
- Analysis of oscillator lattices with periodic boundary conditions.
Main Results:
- Novel synchronization phenomena emerge when time delay and learning effects are combined.
- Spatiotemporal patterns are formed in both 1D and 2D oscillator lattices.
- The dimensionality of the network influences the observed patterns and synchronization.
Conclusions:
- Time delay and Hebbian learning introduce complex dynamics to coupled oscillator systems.
- The interplay between these factors is critical for understanding emergent synchronization and pattern formation.
- Further research into dimensionality's role can illuminate network behavior.
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