Prediction models constructed from state-space dynamics have a long and rich history, dating back to roulette and beyond. A major stumbling block in the application of these models in real-world ...

Introduces undergraduate students to chaotic dynamical systems. Topics include smooth and discrete dynamical systems, bifurcation theory, chaotic attractors, fractals, Lyapunov exponents, ...

In] any piece of beautiful mathematics, you almost always find that there is a physical system which actually mirrors the ...

Example-oriented survey of nonlinear dynamical systems, including chaos. Combines numerical exploration of differential equations describing physical problems with analytic methods and geometric ...

Iteration of a rational function R gives a complex dynamical system on the Riemann sphere. We introduce a C*-algebra 𝓞R associated with R as a Cuntz-Pimsner algebra of a Hilbert bimodule over the ...

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 ...

Imagine a garden filled with every variety of flower in the world — delicate orchids, towering sunflowers, the waxy blossoms of the saguaro cactus and the corpse flower’s putrid eruptions. Now imagine ...

In 1885, King Oscar II of Sweden announced a public challenge consisting of four mathematical problems. The French polymath Henri Poincaré focused on one related to the motion of celestial bodies, the ...

Researchers are using reaction networks and dynamical systems to study these hidden patterns in living systems: Reports ...