Dresden 2011 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 14: Delay Dynamics
DY 14.5: Vortrag
Dienstag, 15. März 2011, 15:00–15:15, ZEU 255
Global bifurcations in delay differential equations with multiple feedback loops — •Ernesto M. Nicola1, Saul Ares2, and Luis G. Morelli3 — 1IFISC, Institute for Cross-Disciplinary Physics and Complex Systems (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain. — 2Max-Planck Institute for the Physics of Complex Systems, Noethnitzer Strasse 38, 01187 Dresden, Germany. — 3Max-Planck Institute of Molecular Cell Biology and Genetics, Pfotenhauerstrasse 108, 01307 Dresden, Germany.
Feedback loops are ubiquitous in dynamical systems. In particular those systems which are capable of showing oscillations are typically based on a negative feedback loop whose effect is not instantaneous but delayed in time. This delayed feedback is usually described by intermediate variables which relay the information and induce an implicit time delay. Added to this delayed negative feedback, systems with realistic applications typically include extra feedback mechanisms. In this contribution we analyze the effect of this extra feedback loops in simple models showing oscillatory behavior. We include explicit time delays in our models to minimize the number of variables and parameters while keeping the richest possible phenomenology in the models. A thorough bifurcation analysis shows that the addition of extra feedback loops results in a number of global bifurcations appearing. These global bifurcations greatly enrich the dynamics of the oscillators under consideration and offer mechanisms to control the oscillatory behavior of the system.