Differential equations and oscillation theory
includes Laboratory of Complex Dynamical Systems
Burylko Oleksandr A.
Leading researcherSenior scientific researcher, doctor of science
email: burilko@imath.kiev.ua
Pokutnyi Oleksander Oleksiyovich
Leading researcherdoctor of science
email: alex_poker@imath.kiev.ua
Prykarpatskyy Yarema
Leading researcherSenior scientific researcher, doctor of science
email: yarpry@imath.kiev.ua
Teplinsky Alexey
Leading researcherSenior scientific researcher, doctor of science
email: teplinsky@imath.kiev.ua
Panchuk Anastasiia
Senior researcherSenior scientific researcher, candidate of science
email: nastyap@imath.kiev.ua
Sushko Iryna Mykhailivna
Senior researcherSenior scientific researcher, candidate of science
email: sushko@imath.kiev.ua
The staff of the Department of Differential Equations and Oscillation Theory, including the Laboratory of Complex Dynamical Systems, continues the traditions of the world-famous mathematical school of nonlinear mechanics (founders - academicians M. M. Krylov and M. M. Bogolyubov).
Until 2020, the department was headed by Academician of the National Academy of Sciences of Ukraine Anatoliy Samoilenko. From 2021 to 2024, the department was headed by Academician of the National Academy of Sciences of Ukraine Oleksandr Boichuk. Since 2024, the head of the department is Professor Viktor Tkachenko.
The main areas of research in the department:
Investigation of the existence, stability and bifurcation of bounded, periodic, almost periodic solutions and invariant sets of differential, functional-differential, evolution and impulsive systems. Asymptotic integration of various classes of differential equations.
Development of constructive methods for the analysis of linear and weakly nonlinear (with a normally solvable linear part) boundary-value problems for a wide class of operator equations, in particular functional-differential, integro-differential, difference, singularly perturbed equations and equations with fractional derivatives.
Research of complex dynamical systems that describe the collective dynamics of interacting objects depending on their individual dynamics, the architecture of the interaction network and the ways in which one element influences another. Study of dynamical regimes, bifurcations and self-organization processes, in particular synchronization, cluster structures, chimera states, regimes of long-term switching between clusters, chaos, heteroclinic structures.
Mathematical modeling and numerical implementation of biological, physical and economic processes using differential and difference equations with smooth, non-smooth and discontinuous right-hand sides.