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Chaos in neural networks with a nonmonotonic transfer function
D Caroppo1, M Mannarelli, G Nardulli
1Dipartimento Interateneo di Fisica and Istituto Nazionale di Fisica Nucleare, Sezione di Bari, via Amendola 173, 70126 Bari, Italy.
Summary
This study analyzes diluted neural networks, revealing complex dynamics like chaos and periodicity. Chaotic behavior in these networks is shown to be fragile, with distinct microscopic states persisting over time.
Area of Science:
- Computational neuroscience
- Complex systems dynamics
Background:
- Diluted neural networks offer a simplified model for studying complex dynamics.
- Nonmonotonic transfer functions can lead to rich emergent behaviors.
Purpose of the Study:
- To analytically describe the time evolution of diluted neural networks with nonmonotonic transfer functions.
- To investigate the macroscopic dynamics, attractor structure, and robustness of chaos.
- To analyze microscopic behavior and damage spreading.
Main Methods:
- Utilizing flow equations for macroscopic variables to model network dynamics.
- Detailed examination of strange attractor properties: manifolds, hyperbolicity, and homoclinic intersections.
- Analysis of damage spreading by comparing near-identical initial configurations.
Main Results:
- Macroscopic dynamics exhibit fixed-point, periodic, and chaotic behaviors.
- Chaotic behavior is proven to be fragile, with periodicity windows interspersed.
- Microscopic states remain distinct over time, regardless of parameter choice, indicating no significant damage spreading.
Conclusions:
- The analytical framework successfully describes complex dynamics in diluted neural networks.
- The fragility of chaos and the persistence of distinct microscopic states are key findings.
- This model provides insights into the fundamental behaviors of neural network dynamics.