Dresden 2006 – scientific programme
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DY: Dynamik und Statistische Physik
DY 34: Nonlinear Dynamics, Synchronization and Chaos I
DY 34.3: Talk
Wednesday, March 29, 2006, 15:00–15:15, H\"UL 186
2-tori and bursting oscillations close to a generalized Hopf bifurcation in the fast subsystem — •Ronny Straube1,2, Dietrich Flockerzi3, Marcus J. B. Hauser2, and Stefan C. Müller2 — 1Abteilung Theoretische Physik, Hahn-Meitner-Institut Berlin, Glienicker Str. 100, 14109 Berlin — 2Abteilung Biophysik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg — 3Max-Planck-Institut für Dynamik komplexer technischer Systeme, Sandtorstr. 1, 39106 Magdeburg
Many chemical and biological systems exhibit bursting behavior which may be conventiently classified by the type bifurcations occuring in the fast subsystem [1]. Using two examples, we demonstrate that, depending on the dynamics of the slow subsystem, the existence of a generalized Hopf bifurcation in the fast subsystem may likewise account for the emergence of bursting oscillations (which are then of subHopf/fold-cycle type) or the emergence of a 2-torus exhibiting a typical phase flow on it. This investigation reveals a common origin of both types of dynamics.
[1] E. M. Izhikevich, Int. J. Bifurcat. Chaos 10 (2000) 1171.