The field of dynamical systems is being transformed by the mathematical tools and
algorithms emerging from modern computing and data science. First-principles derivations …

Significant experimental, computational, and theoretical work has identified rich structure
within the coordinated activity of interconnected neural populations. An emerging challenge …

Data-driven discovery is revolutionizing how we model, predict, and control complex
systems. Now with Python and MATLAB®, this textbook trains mathematical scientists and …

In this work, we demonstrate how physical principles—such as symmetries, invariances and
conservation laws—can be integrated into the dynamic mode decomposition (DMD). DMD is …

SIMPLE aerodynamic configurations under even modest conditions can exhibit complex
flows with a wide range of temporal and spatial features. It has become common practice in …

The integration of data and scientific computation is driving a paradigm shift across the
engineering, natural, and physical sciences. Indeed, there exists an unprecedented …

Electroencephalography (EEG) has been instrumental in making discoveries about
cognition, brain function, and dysfunction. However, where do EEG signals come from and …

Spectral decomposition of the Koopman operator is attracting attention as a tool for the
analysis of nonlinear dynamical systems. Dynamic mode decomposition is a popular …

Understanding the interplay of order and disorder in chaos is a central challenge in modern
quantitative science. Approximate linear representations of nonlinear dynamics have long …

We establish the convergence of a class of numerical algorithms, known as dynamic mode
decomposition (DMD), for computation of the eigenvalues and eigenfunctions of the infinite …