Dynamical systems and chaos theory provide a rigorous mathematical framework to describe, analyse and predict the evolution of systems over time. These fields study how simple deterministic rules can ...

Physicists have proven -- numerically and experimentally -- that turbulence in fluid flows can be understood and quantified with the help of a small set of special solutions that can be precomputed ...

Covers dynamical systems defined by mappings and differential equations. Hamiltonian mechanics, action-angle variables, results from KAM and bifurcation theory, phase plane analysis, Melnikov theory, ...

“One of the most surprising predictions of modern quantum theory is that the vacuum of space is not empty. In fact, quantum theory predicts that it teems with virtual particles flitting in and out of ...

A research team has developed a novel method for estimating the predictability of complex dynamical systems. Their work, "Time-lagged recurrence: A data-driven method to estimate the predictability of ...

Researchers have uncovered an altogether new type of fractal appearing in a class of magnets called spin ices. The discovery was surprising because the fractals were seen in a clean three-dimensional ...

The application of dynamical systems theory to areas outside of mathematics continues to be a vibrant, exciting, and fruitful endeavor. These application areas are diverse and multidisciplinary, ...

A research team developed a satellite -based method to analyze the life cycle of ocean eddies forming along Arctic sea-ice edges. By combining sequential synthetic aperture radar (SAR) images with ...

A system of equations where the output of one equation is part of the input for another. A simple version of a dynamical system is linear simultaneous equations. Non-linear simultaneous equations are ...