Overview of the research activity
Most mathematical models of experimental science are formulated using differential equations. Based on models developed in different scientific areas, Qualitative Theory of Ordinary Differential Equations is one of the tools for understanding these models. This study is implemented through the following objectives: the topological description of their solutions (phase portrait), the long-term behaviour of the solutions (attractors, stable and unstable manifolds) and the change in the structure of the solutions when the parameters vary (bifurcations or chaotic behaviour).
The three main research lines of our group are:
1. Qualitative theory of smoth ODE’s.
2. Qualitative theory of ODE’s systems piecewise linear.
3. Qualitative theory of discrete dynamical systems.
The group of “Sistemes Dinàmics” started its formal activity in 2002. Since then, we have developed our scientific activity in various fields including organization of international congresses, winter schools, research seminars, seminars for the dissemination of our scientific activities, attendance and participation in conferences, plenary lectures, conferences on math disclosure, etc. The seminars for the scientific training for our members, that are open to any interested person, are regularly conducted. The first one dates from March 12, 2003.
At the present time we develop our scientific research jointly with members of the Universidad de Extremadura (UNEX, Spain), sharing a common research project (MTM2014-54275-P Spanish Government Grant) entitled “Estudio cualitativo de sistemas dinámicos y de sus aplicaciones. Comportamientos periódicos y bifurcaciones”.
We also participated in the network DANCE that aims at being the meeting point of the Spanish researchers in Dynamical Systems and nonlinear dynamics with a flexible, open, integrating and interdisciplinary approach.
At the Department of Mathematics and Computer Science (UIB), in the Applied Mathematics field, we share some common goals with the research group “Tractament i Anàlisi Matemàtica d’Imatges (TAMI)” (Mathematical Analysis and Image Processing).
More information: http://www.ssdd.uib.es/