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Exact expression for maximum Lyapunov exponent during transients in computationally powerful dynamical networks

Year: 2026
Type: preprint
Abstract: 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.
DOI: 10.48550/arxiv.2605.21174
Authors: 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.
Institutions: Western University, King’s University College, The King's University, Fields Institute for Research in Mathematical Sciences, Stanford University, Carl von Ossietzky Universität Oldenburg, University of Lethbridge
Open Access status: green
Funders: National Science Foundation, Canada Research Chairs, Canada First Research Excellence Fund, Alliance de recherche numérique du Canada, National Institutes of Health, Natural Sciences and Engineering Research Council of Canada
OpenAlex ID: W7162003299
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