The International Laboratory for Dynamic Systems and Applications was established as part of the Megagrant 220 project of the Government of the Russian Federation in December 2019. From the moment the laboratory was established until December 2022, the scientific director of the laboratory was an outstanding specialist in the theory of dynamical systems and its applications Dmitry Turaev. Since 2023, Vyacheslav Grines, the largest specialist in topological methods in dynamics, has been the scientific director of the laboratory.

The core of the team was a group of teachers-researchers who are actively involved in the qualitative theory of dynamical systems and applications within the school of nonlinear oscillations created by academician A.A. Andronov. The Nizhny Novgorod school, from which both Dmitry Turaev and Vyacheslav Grines come from, was and remains the leader in the theory of dynamical systems due to the unique combination of rigorous methods of topological and geometric analysis with applied studies of nonlinear physical phenomena.

The main aims of the laboratory are to strengthen domestic and international relations, increase the prestige of the scientific school, diversify and update the direction of research, organize effective cooperation between representatives of various disciplines, and support young scientists.