When chaos creates stability

Associate Professor Danijela Damjanovic will receive funding from the Knut and Alice Wallenberg Foundation to recruit an international researcher for a postdoctoral position at the Department of Mathematics, KTH Royal Institute of Technology.

The research field of dynamical systems can be regarded as a bridge between theoretical mathematics and mathematical applications in science. One classic question is how a system will develop over time, which provides predictions about the future. The area, which led to modern chaos theory, was initiated by Frenchman Henri Poincaré. In a pioneering work at the end of the 18th century, he showed that systems such as the solar system or just three celestial bodies moving according to Newton’s gravity laws, need not be stable. He received a prize from King Oscar II for this work.

Despite Poincaré’s discoveries, chaos was long thought to be just an aberration. The planned project builds upon groundbreaking discoveries made in the 1960s, which showed that chaos can also be a source of stability in because it turns out to be difficult to perturb. These discoveries are the basis for a new view on how a biologist looks at a healthy heart rhythm, or what a healthy brain is, or how physicists interpret their data.

For systems with multidimensional time called group actions the relationship between chaos and stability is even more dramatic: weaker chaotic behavior can lead to stronger system stability. Such systems are useful models in biology (neural networks), chemistry (quasi-crystals) and computer science (multi-dimensional data storage). Chaos occurs in different forms in different models. The purpose of this project is to explore the conditions under which systems with different chaotic behavior maintain their dynamic characteristics when disturbed.