Abstract: Among the invariant characteristics of dynamical systems, an important role is played by the Lyapunov exponents and the Lyapunov dimension. The analysis of the spectrum of Lyapunov exponents is widely used to study complex dynamics in systems of ordinary differential equations and in models that reduce to mappings. In the finite-dimensional case, according to the Oseledets theorem, the system of ordinary differential equations linearized on an attractor is always Lyapunov stable, and thus the upper limit can be replaced by the ordinary one, which makes it possible to effectively calculate the Lyapunov exponents. In this talk, it is planned to consider the question of calculating Lyapunov exponents for systems of differential equations of argument with delay, for which the theorem in general does not work. The results of testing the developed algorithm for the Hutchinson equation will be presented and an application of the algorithm to some problems will be illustrated.
Location: Znam. tower, 3 Komsomol'skaya rd. (entrance inside the arch).