Delayed Linear Analysis for Stability Estimation code

This repository contains code for running the DeLASE algorithm (Delayed Linear Analysis for Stability Estimation). DeLASE was designed to quantify changes in population-level stability in complex systems. DeLASE harnesses the power of Koopman operators (namely, the HAVOK algorithm¹) to efficiently generate linear representations of nonlinear dynamics. DeLASE then reformulates the Koopman operator as a delay dynamical system, and utilizes tools (namely, the TRACE-DDE algorithm) from delay differential equations theory for estimating the stability of such equations².

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1. Brunton, S.L., Brunton, B.W., Proctor, J.L., Kaiser, E., and Kutz, J.N. (2017). Chaos as an intermittently forced linear system. Nat. Commun. 8, 19.
2. Breda, D., Maset, S., and Vermiglio, R. (2009). TRACE-DDE: a Tool for Robust Analysis and Characteristic Equations for Delay Differential Equations. In Topics in Time Delay Systems: Analysis, Algorithms and Control, J. J. Loiseau, W. Michiels, S.-I. Niculescu, and R. Sipahi, eds. (Springer Berlin Heidelberg), pp. 145–155.