Researchers - employees:
Jan Čermák, Tomáš Kisela, Luděk Nechvátal, Pavel Řehák, Petr Tomášek

Researchers - doctoral students:
Lucie Fedorková 

Annotation
The group has long been dealing with qualitative and numerical analysis of ordinary differential equations of integer and non-integer orders, including equations involving the time delay factor. Key topics include linear and nonlinear differential equations, dynamic equations on time scales, stability, oscillations and asymptotics of their solutions, regular variations, dynamic systems and their control (stabilization, destabilization, chaotification, synchronization), numerical discretization.

Formal outputs
Members of the group participate in solving GAČR projects as part of long-term cooperation with Masaryk University (the currently solved project ends this year, an application for a new grant competition was submitted). They publish the results in professional journals with a large readership, or in monographs, primarily in the form of co-authorship (within the group, or as part of collaboration with foreign experts). They also participate in the development of regular academic life (organization of seminars, conferences, serving on the editorial boards of professional journals).

Foreign cooperation
The University of Florence (S. Matucci), The University of Modena (V. Taddei, L. Malaguti), Osaka Metropolitan University (H. Matsunaga, N. Yamaoka).

Cooperation with other departments/groups at ÚM
This group is open to any professional cooperation within the institute (and outside it).   The nature of our research offers contact topics in the field of mathematical analysis (especially complex and functional), numerical mathematics (including programming), (linear) algebra, probability theory (non-Gaussian probability distributions when solving fractional models, asymptotically scale invariance), fuzzy logic (fuzzy management of fractional systems), or in the issue of fractals (graphical visualization of the solution of chaotic dynamic systems). This naturally opens up space for cooperation with experts in the mentioned areas, while such cooperation has already been implemented within the ÚM.

 
Scientific preparation of bachelor's and master's students
The writing of theses topics is to some extent coordinated within the group. Topics are listed either in direct connection to the research being conducted (usually numerical simulations of obtained theoretical results, or their other support), or from the basic areas of this research. However, the group also offers original topics from other areas of mathematics, the main purpose of which is to support students' interest in the field of mathematical engineering.