Essentially asymptotically stable homoclinic networks

R. Driesse, A.J. Homburg

Research output: Contribution to JournalArticleAcademicpeer-review


Melbourne [An example of a nonasymptotically stable attractor, Nonlinearity 4(3) (1991), pp. 835-844] discusses an example of a robust heteroclinic network that is not asymptotically stable but which has the strong attracting property called essential asymptotic stability. We establish that this phenomenon is possible for homoclinic networks, where all heteroclinic trajectories are symmetry related. Moreover, we study a transverse bifurcation from an asymptotically stable to an essentially asymptotically stable homoclinic network. The essentially asymptotically stable homoclinic network turns out to attract all nearby points except those on codimension-one stable manifolds of equilibria outside the homoclinic network.
Original languageEnglish
Pages (from-to)459-471
JournalDynamical Systems-an International Journal
Issue number4
Publication statusPublished - 2009


Dive into the research topics of 'Essentially asymptotically stable homoclinic networks'. Together they form a unique fingerprint.

Cite this