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ON DYNAMIC MODE DECOMPOSITION: THEORY AND …

Manuscript submitted to the Journal of Computational DynamicsON DYNAMIC MODE DECOMPOSITION: THEORY AND APPLICATIONSJ onathan H. Tu, Clarence W. Rowley, Dirk M. Luchtenburg,Dept. of Mechanical and Aerospace EngineeringPrinceton UniversityPrinceton, NJ 08544, USAS teven L. Brunton, and J. Nathan KutzDept. of Applied MathematicsUniversity of WashingtonSeattle, WA 98195, introduced in the fluid mechanics community, dynamicmode decomposition (DMD) has emerged as a powerful tool for analyzing thedynamics of nonlinear systems. However, existing DMD THEORY deals primarilywith sequential time series for which the measurement dimension is much largerthan the number of measurements taken.

The remainder of this work is organized as follows: in Section2, we propose and discuss a new de nition of DMD. We provide several di erent algorithms for com-puting DMD modes and eigenvalues that satisfy this new de nition and show that these are closely related to the modes and eigenvalues computed using the currently

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  Dome, Dynamics, Theory, Theory and, Remainder, Decomposition, Dynamic mode decomposition

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