Exact expression for maximum Lyapunov exponent during transients in computationally powerful dynamical networks
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arXiv
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| Auteurs principaux: | , , , , , , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914583166320640 |
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| author | Powanwe, Arthur S. Liboni, Luisa H. B. Shikder, Anif N. Busch, Alexandra N. Rossi, Kalel L. Coleman, Todd Mináč, Ján Feudel, Ulrike Budzinski, Roberto C. Muller, Lyle E. |
| author_facet | Powanwe, Arthur S. Liboni, Luisa H. B. Shikder, Anif N. Busch, Alexandra N. Rossi, Kalel L. Coleman, Todd Mináč, Ján Feudel, Ulrike Budzinski, Roberto C. Muller, Lyle E. |
| contents | We study a network whose rich spatiotemporal dynamics have recently been shown to enable dynamics-based computation, including logic gates, short-term memory, and simple encryption. The network's time dynamics can be exactly solved through a nonlinear coordinate transformation. Here, we derive an exact analytical expression for the network's time-dependent maximum Lyapunov exponent (MLE). We demonstrate, both numerically and analytically, that the network exhibits positive MLEs during the transients that are useful for computation. Our framework enables algebraic manipulation of transient lifetimes through network connectivity and initial conditions, providing a rigorous theoretical foundation for understanding and controlling computation with transients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21174 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exact expression for maximum Lyapunov exponent during transients in computationally powerful dynamical networks Powanwe, Arthur S. Liboni, Luisa H. B. Shikder, Anif N. Busch, Alexandra N. Rossi, Kalel L. Coleman, Todd Mináč, Ján Feudel, Ulrike Budzinski, Roberto C. Muller, Lyle E. Chaotic Dynamics Adaptation and Self-Organizing Systems We study a network whose rich spatiotemporal dynamics have recently been shown to enable dynamics-based computation, including logic gates, short-term memory, and simple encryption. The network's time dynamics can be exactly solved through a nonlinear coordinate transformation. Here, we derive an exact analytical expression for the network's time-dependent maximum Lyapunov exponent (MLE). We demonstrate, both numerically and analytically, that the network exhibits positive MLEs during the transients that are useful for computation. Our framework enables algebraic manipulation of transient lifetimes through network connectivity and initial conditions, providing a rigorous theoretical foundation for understanding and controlling computation with transients. |
| title | Exact expression for maximum Lyapunov exponent during transients in computationally powerful dynamical networks |
| topic | Chaotic Dynamics Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2605.21174 |