Tutorials & GUIs ... Windowing and Leakage 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 ...

Here we develop a self-consistent theory of dynamical perturbations in complex systems, allowing us to systematically separate the contribution of the network topology and dynamics.

Tutorials & GUIs Fourier Series 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 ...

Michael Dellnitz, Oliver Junge, On the Approximation of Complicated Dynamical Behavior, SIAM Journal on Numerical Analysis, Vol. 36, No. 2 (Jan. - Mar., 1999), pp ...

APPM 5460 Methods in Applied Mathematics: Dynamical Systems and Differential Equations Introduces the theory and applications of dynamical systems through solutions to differential equations.Covers ...

Such systems may be chaotic, consisting of regions in phase space of stable, regular motion embedded in a sea of chaos. Previous studies predicted4 dynamical tunnelling between these stable regions.

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 ...

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 ...

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 ...