Windows are a tool commonly used in frequency domain signal processing to preserve the amplitude of a signal and/or minimize leakage. In Dynamic Systems work, windows are useful for determining the ...

The Fourier Series is a mathematical tool which is commonly used for solving many different engineering problems. In Dynamic Systems work, the Fourier Series is useful for understanding frequency ...

Despite significant advances in characterizing the structural properties of complex networks, a mathematical framework that uncovers the universal properties of the interplay between the topology and ...

Introduces the theory and applications of dynamical systems through solutions to differential equations.Covers existence and uniqueness theory, local stability properties, qualitative analysis, global ...

The course will survey methods for characterizing time-series data by reading primary literature and implementing and testing methods on synthetic data. Students will simulate time-series from a ...

SIAM Journal on Numerical Analysis, Vol. 36, No. 2 (Jan. - Mar., 1999), pp. 491-515 (25 pages) We present efficient techniques for the numerical approximation of complicated dynamical behavior. In ...

A continuous map on a compact metric space, regarded as a dynamical system by iteration, admits invariant measures. For a closed relation on such a space, or, equivalently, an upper semicontinuous set ...

Scientists usually use a hypergraph model to predict dynamic behaviors. But the opposite problem is interesting, too. What if researchers can observe the dynamics but don't have access to a reliable ...

Researchers from Osaka University have developed an artificial intelligence algorithm that discovers the underlying conservation laws of real-world dynamical systems, not just the superficial dynamics ...