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Bursting as an emergent phenomenon in coupled chaotic maps
1Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1. devries@math.ualberta.ca
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 12, 2001
Summary
Coupling non-bursting cells via mean-field interactions can restore chaotic bursting behavior, mimicking biological electrical activity. This emergent phenomenon is robust and independent of individual cell parameter variations.
Area of Science:
- Computational neuroscience
- Nonlinear dynamics
- Systems biology
Background:
- Biological neurons and endocrine cells exhibit complex electrical bursting patterns.
- A two-dimensional map model displays chaotic bursting behavior.
- Individual model cells were modified to eliminate this bursting behavior.
Purpose of the Study:
- To investigate the recovery of bursting behavior in a population of non-bursting cells.
- To understand the role of network coupling in emergent dynamics.
- To analyze the robustness of this phenomenon.
Main Methods:
- Mathematical modeling of a two-dimensional map system.
- Parameter modification to destroy intrinsic bursting.
- Network coupling via mean-field interactions.
- Geometric bifurcation analysis.
Main Results:
- Coupling non-bursting cells via mean-field interactions successfully restores chaotic bursting.
- Emergent bursting is solely a consequence of network coupling.
- The phenomenon is highly robust to variations in coupling strength.
- Heterogeneity in individual cell parameters does not influence the emergent bursting.
Conclusions:
- Mean-field coupling is sufficient to induce robust bursting dynamics in non-bursting units.
- Network interactions can generate complex behaviors not present in individual components.
- This finding has implications for understanding collective dynamics in biological and artificial systems.
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