Research in dynamic systems theory is conducted at the Laboratory of Ordinary Differential Equation in the following directions:
- non-linear boundary value problems,
- qualitative research of ordinary differential systems and their generalizations including in Banach space,
- linear and non-linear eigenvalue problems,
- dynamic equations on time scales,
- qualitative analysis of difference equations,
- equations in network regulatory theory.
The research is aimed at studies in the field of dynamic and difference systems and equations. Priority is given to those theoretical directions which are predictably of practical significance in the foreseeable future. As instances the specific tasks such as self-similar solutions and the respective transformations for Blasius and Falkner - Skan type differential equations or investigation of Fuchik type spectra for asymmetrical differential equations can be pointed out. As well the study of attracting sets for nonlinear dynamical systems of gene regulatory networks can be pointed out. These types of research require detailed and labour-intensive analysis. The goal is to continue theoretical studies in selected directions and to publish the results in anonymously refereed editions and report them at Europe-wide mathematical forums. The hypotheses and directions of research in each individual case are to be specified in agenda. The methodology is based on strict mathematical analysis with explanatory-illustrative computational experiments.
The theory of time scales was introduced in order to unify continuous and discrete analysis of dynamic equations. The study of dynamic equations on time scales helps avoiding proving results twice, once for differential equations and once for difference equations.
Sub-branches:
Nonlinear boundary value problems.
Qualitative research of ordinary differential systems and their generalizations including in Banach space.
Linear and non-linear eigenvalue problems: The main attention is paid to boundary value problems for linear differential equations of the Fučík type and non-linear asymptotically asymmetric differential equations containing parameters.
Dynamic equations on time scales.
Qualitative analysis of difference equations.
Equations in network regulatory theory: Systems of ordinary differential equations arising in the network regulatory theory and possessing attracting sets are considered. The structure of attractors is studied, as well as their dependence on parameters and their role in self-regulation of related networks.
Read more: http://www.lumii.lv/14/10s/
Leading researchers: Andrejs Reinfelds, Felix Sadyrbaev, Svetlana Atslēga, Inese Bula, Natālija Sergejeva, Sergey Smirnov.