Stability of heteroclinic networks
 
 
Description:  Invariant sets are important objects in the study of dynamical systems since they allow us to describe families of trajectories/solutions. In fact, a solution starting in an invariant set will remain in this set for all time. Whether this solution is complex or simple depends on the complexity, or simplicity, of the invariant set. Another important concept in the study of dynamical systems is that of stability. This goes back to Lyapunov at the end of the 19th century. When an invariant set is stable, it can be used to retrieve information not only about solutions belonging to it but also to study nearby solutions (which, because of stability, will tend to the invariant set in the future).
In this talk the objects of interest are heteroclinic networks, that is, a collection of equilibria and the connections amongst them, as well as the study of solutions near the heteroclinic connection. The behaviour of these nearby solutions is especially interesting when the heteroclinic network is somewhat, but not asymptotically, stable. I shall discuss various notions of stability for a heteroclinic network and present examples of the behaviour of nearby solutions in each case.
Date:  2013-03-19
Start Time:   11:30
Speaker:  Sofia Castro (Fac. Economia, Univ. Porto)
Institution:  Faculdade de Economia da Universidade do Porto
Place:  sala 2.5 (DMUC)
See more:   <Main>   <Research Seminar Program - UC|UP MATH PhD Program>  
 
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