We are not able to resolve this OAI Identifier to the repository landing page. If you are the repository manager for this record, please head to the Dashboard and adjust the settings.
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Doi
Abstract
Interaction via pulses is common in many natural systems, especially
neuronal. In this article we study one of the simplest possible systems with
pulse interaction: a phase oscillator with delayed pulsatile feedback. When
the oscillator reaches a specific state, it emits a pulse, which returns
after propagating through a delay line. The impact of an incoming pulse is
described by the oscillators phase reset curve (PRC). In such a system we
discover an unexpected phenomenon: for a sufficiently steep slope of the PRC,
a periodic regular spiking solution bifurcates with several multipliers
crossing the unit circle at the same parameter value. The number of such
critical multipliers increases linearly with the delay and thus may be
arbitrary large. This bifurcation is accompanied by the emergence of numerous
jittering regimes with non-equal interspike intervals (ISIs). The number of
the emergent solutions increases exponentially with the delay. We describe
the combinatorial mechanism that underlies the emergence of such a variety of
solutions. In particular, we show how each periodic solution consisting of
different ISIs implies the appearance of multiple other solutions obtained by
rearranging of these ISIs. We show that the theoretical results for phase
oscillators accurately predict the behavior of an experimentally implemented
electronic oscillator with pulsatile feedback
Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.