4,991 research outputs found
Moving bumps in theta neuron networks
We consider large networks of theta neurons on a ring, synaptically coupled
with an asymmetric kernel. Such networks support stable "bumps" of activity,
which move along the ring if the coupling kernel is asymmetric. We investigate
the effects of the kernel asymmetry on the existence, stability and speed of
these moving bumps using continuum equations formally describing infinite
networks. Depending on the level of heterogeneity within the network we find
complex sequences of bifurcations as the amount of asymmetry is varied, in
strong contrast to the behaviour of a classical neural field model.Comment: To appear in Chao
Amplitude Death: The emergence of stationarity in coupled nonlinear systems
When nonlinear dynamical systems are coupled, depending on the intrinsic
dynamics and the manner in which the coupling is organized, a host of novel
phenomena can arise. In this context, an important emergent phenomenon is the
complete suppression of oscillations, formally termed amplitude death (AD).
Oscillations of the entire system cease as a consequence of the interaction,
leading to stationary behavior. The fixed points that the coupling stabilizes
can be the otherwise unstable fixed points of the uncoupled system or can
correspond to novel stationary points. Such behaviour is of relevance in areas
ranging from laser physics to the dynamics of biological systems. In this
review we discuss the characteristics of the different coupling strategies and
scenarios that lead to AD in a variety of different situations, and draw
attention to several open issues and challenging problems for further study.Comment: Physics Reports (2012
Effects of non-resonant interaction in ensembles of phase oscillators
We consider general properties of groups of interacting oscillators, for
which the natural frequencies are not in resonance. Such groups interact via
non-oscillating collective variables like the amplitudes of the order
parameters defined for each group. We treat the phase dynamics of the groups
using the Ott-Antonsen ansatz and reduce it to a system of coupled equations
for the order parameters. We describe different regimes of co-synchrony in the
groups. For a large number of groups, heteroclinic cycles, corresponding to a
sequental synchronous activity of groups, and chaotic states, where the order
parameters oscillate irregularly, are possible.Comment: 21 pages, 7 fig
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