Hierarchy of Chaotic Dynamics in Random Modular Networks
Łukasz Kuśmierz1, Ulises Pereira-Obilinovic1, Zhixin Lu1
1Allen Institute, Seattle, Washington, USA.
Physical Review Letters
|April 25, 2025
Summary
We explored neural population dynamics, finding that chaos can be reduced by adding noise or modularity. A balance across hierarchical levels drives systems toward the edge of chaos.
Area of Science:
- Computational neuroscience
- Complex systems theory
Background:
- Neural population dynamics are crucial for brain function.
- Understanding the relationship between connectivity and chaotic dynamics is an ongoing challenge.
Purpose of the Study:
- To investigate the phase diagram and dynamics of randomly connected neural populations.
- To explore how connectivity structure influences chaotic behavior.
- To examine the impact of hierarchical connectivity on system stability.
Main Methods:
- Development of a model for randomly connected neural populations.
- Application of dynamical mean-field theory.
- Conducting numerical simulations to analyze system dynamics.
Main Results:
- Identification of a rich phase diagram with distinct high- and low-dimensional chaotic phases.
- Characterization of a crossover region with specific Lyapunov and dimension values.
- Demonstration that noise or modularity can attenuate chaos in neural networks.
- Observation that hierarchical connectivity drives systems toward the edge of chaos.
Conclusions:
- Connectivity structure plays a critical role in shaping neural population dynamics.
- The edge of chaos may be a key operational regime for complex neural systems.
- Modularity and noise can be leveraged to control chaotic dynamics in neural networks.
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