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 ...

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 ...

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 ...

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

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 ...

We often encounter nonlinear dynamical systems that behave unpredictably, such as the earth's climate and the stock market. To analyze them, measurements taken over time are used to reconstruct the ...

Researchers at the University of Toronto have made a significant step towards enabling reliable predictions of complex dynamical systems when there are many uncertainties in the available data or ...

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 ...