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Using a reservoir computer to learn chaotic attractors, with applications to chaos synchronization and cryptography
Piotr Antonik1,2, Marvyn Gulina3, Jaël Pauwels4,5
1CentraleSupélec, Campus de Metz, Université Paris Saclay, F-57070 Metz, France.
Physical Review. E
|August 17, 2018
Summary
Reservoir computing, a machine learning method, trains dynamical systems to emulate chaotic ones. Trained systems achieve chaos synchronization and can break chaos-based cryptography.
Area of Science:
- Dynamical systems theory
- Machine learning
- Chaos theory
Background:
- Reservoir computing enables one dynamical system to emulate another.
- Chaotic systems possess complex attractors that are challenging to model.
- Chaos synchronization involves two chaotic systems aligning their dynamics.
Purpose of the Study:
- To demonstrate that trained reservoir computers can reproduce chaotic system attractors.
- To show chaos synchronization between a trained reservoir computer and a chaotic system.
- To explore the application of trained reservoir computers in cryptanalysis.
Main Methods:
- Utilizing reservoir computing to train a dynamical system to emulate chaotic systems.
- Analyzing the attractor properties of the trained reservoir computer.
- Investigating chaos synchronization via weak driving in both directions.
- Applying trained reservoir computers to a chaos-based cryptosystem.
Main Results:
- Trained reservoir computers accurately reproduce chaotic system attractor properties.
- Successful demonstration of chaos synchronization with both Mackey-Glass and Lorenz systems.
- Trained reservoir computers successfully decrypted a chaos-based cryptosystem.
Conclusions:
- Reservoir computing effectively emulates chaotic systems, enabling synchronization.
- The ability to emulate chaotic dynamics makes reservoir computers potent for cryptanalysis.
- Further research is warranted to understand the underlying reasons for reservoir computers' efficacy with chaotic systems.
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