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Rhythmic behavior in a two-population mean-field Ising model.
Francesca Collet1, Marco Formentin2, Daniele Tovazzi2
1Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands.
Physical Review. E
|November 15, 2016
Summary
Simple interactions between two groups of spins can create regular rhythms in large systems. This study explores how differing interaction strengths drive collective periodic behavior in complex systems.
Area of Science:
- Statistical physics
- Complex systems dynamics
- Computational neuroscience
Background:
- Many-component systems, like neural networks, can show collective periodic behavior.
- Macroscopic oscillations are common in self-organized living systems.
Purpose of the Study:
- Investigate simple mechanisms for generating rhythms in large interacting groups.
- Analyze dynamical features of a two-population mean-field Ising model.
Main Methods:
- Studied a two-population generalization of the mean-field Ising model.
- Examined parameter space for transitions between disordered and rhythmic phases.
Main Results:
- Identified a transition from a disordered phase (magnetization near zero) to a phase with macroscopic regular rhythms.
- Found that differing inter- and intrapopulation interaction strengths can induce robust periodic behavior.
Conclusions:
- Simple mechanisms, specifically varied interaction strengths between spin populations, are sufficient for emergent periodic behavior.
- The findings offer insights into rhythm generation in biological and artificial systems.
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