ELFT HÍRADÓ

[StatFizSzeminar <statfiz AT glu.elte.hu>]

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             ELTE TTK Fizikai Intézet
         STATISZTIKUS FIZIKAI SZEMINÁRIUM


                  2018. szeptember 19.
                     szerda, 11.00 

                   Ulrike Feudel                

              University of Oldenburg

         "Extreme Events in delay-coupled 
           FitzHugh-­Nagumo  Oscillators"

The study of extreme events has gained increasing at-
tention in recent years due to its ubiquitous appear-
ance in a wide variety of important physical situa-
tions ranging from natural disasters to financial 
crises. Previous studies have indicated many factors 
and mechanisms which may cause such rare, recurrent, 
aperiodic events which have a large impact on dynami-
cal systems. Some of these include progressive spatial
synchronization and an interior crisis in networks of
non-identical relaxation oscillators.

An important factor which often shapes the dynamics of
systems in which such extreme events are observed is 
time delayed coupling. For instance, neural activities 
across different regions of the brain - whose synchrony
may lead to epileptic seizures - are coupled by time de-
layed coupling. Moreover, as the flow of information in 
these networks might take different routes to travel from
the source to the destination, more than one delay could
be associated with a single pair of nodes. The impact of
these time-delayed couplings on the emergence of extreme
events has not yet been analyzed. In this talk, we inves-
tigate if delay couplings alone can induce extreme events
in excitable systems.

To study the impact of such delay-couplings, we investi-
gate a system of two identical FitzHugh-Nagumo oscillators
diffusively coupled by single or multiple delays. We show 
that such a system shows rich dynamics which comprises of
in-phase and out-of-phase extreme events. The stability of
the synchronization manifold and its invariant subsets 
plays a crucial role in determining the qualitative nature 
of the dynamics. We also identify that the region in param-
eter space where extreme events are observed; is sandwiched
by two particular bifurcations: a bubbling transition and
a blowout bifurcation. Another striking feature of the events
of the second category is the loss of synchrony significantly
prior to the actual event. This allows us to use the phase 
difference between the oscillators as a precursor to such
an extreme event.


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