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This repository contains the MATLAB files to reproduce the data and figures from Sparse Identification of Slow Timescale Dynamics by Jason J. Bramburger, Daniel Dylewsky, and J. Nathan Kutz (2020). Computations use the publicly available SINDy architecture found at https://faculty.washington.edu/kutz/page26/ and should be stored in a folder entitled 'Util'. Fast periods are found using the sliding-window DMD method from Dynamic mode decomposition for multiscale nonlinear physics by Daniel Dylewsky, Molei Tao, and J. Nathan Kutz (Phys. Rev. E, 2020) for which the associated codes can be found at GitHub/dylewsky/MultiRes_Discovery.

The scripts associated with this repository are as follows:

• ToyModel_sim.m: Generates the toy model data by numerically integrating the differential equation.

• ToyModel_SINDy.m: Continuous-time discovery of a SINDy model to fit the toy model signal. Data is generated by the script ToyModel_sim.m. Corresponds to work in Section II.

• ToyModel_SlowForecast.m: Discovery of a discrete-time mapping for the coarse-grained evolution of the toy model data. Data is generated by the script ToyModel_sim.m. Data is loaded from toy_model_data.mat. Corresponds to work in Section II.

• Logistic_SlowDiscovery.m: Slow timescale discovery for the singularly perturbed logistic ODE. Corresponds to work in Section III A.

• Jupiter_SlowDiscovery.m: Slow timescale discovery for the evolution of Jupiter in its orbital plane. Data is loaded from jupiter_data.mat. Corresponds to work in Section III B.

• Saturn_SlowDiscovery.m: Slow timescale discovery for the evolution of Saturn in its orbital plane. Data is loaded from saturn_data.mat. Corresponds to work in Section III B.

• Chaos_SlowDiscovery.m: Slow timescale discovery for the evolution of a signal with chaotic slow dynamics. Corresponds to work in Section III C.