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Dynamics induced by state-dependent delays — and how to deal with it

joint work with Renato Calleja (IIMAS) and Tony Humphries (McGill)

por el

Dr. Bernd Krauskopf

University of Auckland

Resumen:
Delay differential equations (DDEs) are the mathematical models of choice in applications where delays arise naturally, for example, due to the time it takes different subsystems to communicate, process information and finally react. The delays that are encountered are usually modelled as constant. This may be a good approximation, but communication/processing times may well depend on the state of the system in a significant way, meaning that the delays change dynamically and the governing DDE is state dependent. We present here a case study of a scalar DDE with two delayed feedback terms that depend linearly on the state. The associated constant-delay DDE, obtained by freezing the state dependence, is linear and without recurrent dynamics. With state dependent delay terms, on the other hand, the DDE shows very complicated dynamics. A bifurcation analysis reveals interacting Hopf bifurcations, two-frequency dynamics on invariant tori and associated resonance tongues. Our results may serve as a ‘health warning’: state dependence alone is actually capable of generating a wealth of dynamical phenomena. Hence, it must be taken seriously in applications. On the other hand, as this talk will also demonstrate, tools from bifurcation theory and associated numerical methods are now available to deal effectively with state-dependent delays. This means that there is no need to avoid/disregard state dependence in DDE models.

Jueves 10 de agosto, 2017
13:00 hrs.
Auditorio Carlos Graef, Facultad de Ciencias, UNAM

Informes: coloquiomym@gmail.com, o al 5622-3564.