Scientific seminar: "Clustering of dynamical regimes in 2D and 3D maps using machine learning methods"

Speakers: P.O. Shuvalova, LTMD – NRU HSE Nizhny Novgorod; Stankevich N.V, LTMD – NRU HSE Nizhny Novgorod;

One of the fundamental problems of nonlinear dynamics in the study of dynamical systems is the classification of various types of behavior. Behavior can be conventionally divided into three groups: (i) stationary, i.e., a stable equilibrium state that does not change over time; (ii) periodic, which repeats after a certain time or a number of iterations; (iii) non-periodic, when a point does not return to the same state from which it started. Classifying the first two groups is a fairly simple task, although some difficulties may arise for some systems, for example, with periodic oscillations of a very long period. The third group may include various types of oscillatory activity, for the classification of which other metrics can be used, for example, Lyapunov exponents, with the help of which we can distinguish between quasi-periodic, chaotic, and hyperchaotic oscillations. Moreover, within this class, we can distinguish, for example, homoclinic attractors, which can no longer be distinguished by Lyapunov exponents, but they may have other characteristics that can be used to classify them. Collecting and analyzing data on various attractors can provide new opportunities for solving clustering and classifying dynamic regimes. The seminar will discuss the results obtained during the first stage of the project on the use of machine learning methods for attractor clustering, using two-dimensional and three-dimensional mappings as examples.