Computing Heteroclinic Orbits for Dynamical Systems
This course provides an overview of the most well known methods for computing heteroclinic orbits for dynamical systems.
Overview
This talk focuses on the computation of heteroclinic orbits in nonlinear dynamical systems, highlighting their significance as connections between distinct equilibria. After a brief review of some basic phase-space concepts, we discuss why heteroclinic connections are central to understanding transitions, pattern formation, and bifurcations in applied models. The main emphasis is on numerical approaches—such as shooting methods, boundary-value formulations with collocation, and other techniques. Low-dimensional examples will be presented from applications in biology and physics.
Presenters
Theodoros Katsaounis, Professor, Department of Mathematics and Applied Mathematics, University of Crete (UoC)
Brief Biography
Dr. Theodoros Katsaounis is a Professor of Mathematics at the University of Crete. He received his Ph.D in 1994 for the Univ. of Tennessee USA, in applied mathematics. After his postdoctoral studies in the Ecole Normale Superieure of Paris, he joined the Deptartment of Applied Mathematics of University of Crete, Greece as an Assistant professor in 2003. Dr. Katsaounis was a Research Scientist at KAUST from 2015 to 2020. His research interests are in the area of applied and computational mathematics with emphasis on the development, analysis and implementation of numerical methods for approximating solutions of PDE’s modelling various physical processes.
