64 research outputs found
Self-organization of network dynamics into local quantized states
Self-organization and pattern formation in network-organized systems emerges
from the collective activation and interaction of many interconnected units. A
striking feature of these non-equilibrium structures is that they are often
localized and robust: only a small subset of the nodes, or cell assembly, is
activated. Understanding the role of cell assemblies as basic functional units
in neural networks and socio-technical systems emerges as a fundamental
challenge in network theory. A key open question is how these elementary
building blocks emerge, and how they operate, linking structure and function in
complex networks. Here we show that a network analogue of the Swift-Hohenberg
continuum model---a minimal-ingredients model of nodal activation and
interaction within a complex network---is able to produce a complex suite of
localized patterns. Hence, the spontaneous formation of robust operational cell
assemblies in complex networks can be explained as the result of
self-organization, even in the absence of synaptic reinforcements. Our results
show that these self-organized, local structures can provide robust functional
units to understand natural and socio-technical network-organized processes.Comment: 11 pages, 4 figure
Chimera states in heterogeneous networks
Chimera states in networks of coupled oscillators occur when some fraction of
the oscillators synchronise with one another, while the remaining oscillators
are incoherent. Several groups have studied chimerae in networks of identical
oscillators, but here we study these states in a heterogeneous model for which
the natural frequencies of the oscillators are chosen from a distribution. We
obtain exact results by reduction to a finite set of differential equations. We
find that heterogeneity can destroy chimerae, destroy all states except
chimerae, or destabilise chimerae in Hopf bifurcations, depending on the form
of the heterogeneity.Comment: Revised text. To appear, Chao
Spike-burst chimera states in an adaptive exponential integrate-and-fire neuronal network
We wish to acknowledge the support from Fundação Araucária, CNPq (Grant No. 150701/2018-7), CAPES, and FAPESP (Grant Nos. 2015/07311-7, 2018/03211-6, and 2017/18977-1).Peer reviewedPublisher PD
Controlling Chimeras
Coupled phase oscillators model a variety of dynamical phenomena in nature
and technological applications. Non-local coupling gives rise to chimera states
which are characterized by a distinct part of phase-synchronized oscillators
while the remaining ones move incoherently. Here, we apply the idea of control
to chimera states: using gradient dynamics to exploit drift of a chimera, it
will attain any desired target position. Through control, chimera states become
functionally relevant; for example, the controlled position of localized
synchrony may encode information and perform computations. Since functional
aspects are crucial in (neuro-)biology and technology, the localized
synchronization of a chimera state becomes accessible to develop novel
applications. Based on gradient dynamics, our control strategy applies to any
suitable observable and can be generalized to arbitrary dimensions. Thus, the
applicability of chimera control goes beyond chimera states in non-locally
coupled systems
Chimera states in networks of phase oscillators: the case of two small populations
Chimera states are dynamical patterns in networks of coupled oscillators in
which regions of synchronous and asynchronous oscillation coexist. Although
these states are typically observed in large ensembles of oscillators and
analyzed in the continuum limit, chimeras may also occur in systems with finite
(and small) numbers of oscillators. Focusing on networks of phase
oscillators that are organized in two groups, we find that chimera states,
corresponding to attracting periodic orbits, appear with as few as two
oscillators per group and demonstrate that for the bifurcations that
create them are analogous to those observed in the continuum limit. These
findings suggest that chimeras, which bear striking similarities to dynamical
patterns in nature, are observable and robust in small networks that are
relevant to a variety of real-world systems.Comment: 13 pages, 16 figure
Bistable Chimera Attractors on a Triangular Network of Oscillator Populations
We study a triangular network of three populations of coupled phase
oscillators with identical frequencies. The populations interact nonlocally, in
the sense that all oscillators are coupled to one another, but more weakly to
those in neighboring populations than to those in their own population. This
triangular network is the simplest discretization of a continuous ring of
oscillators. Yet it displays an unexpectedly different behavior: in contrast to
the lone stable chimera observed in continuous rings of oscillators, we find
that this system exhibits \emph{two coexisting stable chimeras}. Both chimeras
are, as usual, born through a saddle node bifurcation. As the coupling becomes
increasingly local in nature they lose stability through a Hopf bifurcation,
giving rise to breathing chimeras, which in turn get destroyed through a
homoclinic bifurcation. Remarkably, one of the chimeras reemerges by a reversal
of this scenario as we further increase the locality of the coupling, until it
is annihilated through another saddle node bifurcation.Comment: 12 pages, 5 figure
Multiscale Computations on Neural Networks: From the Individual Neuron Interactions to the Macroscopic-Level Analysis
We show how the Equation-Free approach for multi-scale computations can be
exploited to systematically study the dynamics of neural interactions on a
random regular connected graph under a pairwise representation perspective.
Using an individual-based microscopic simulator as a black box coarse-grained
timestepper and with the aid of simulated annealing we compute the
coarse-grained equilibrium bifurcation diagram and analyze the stability of the
stationary states sidestepping the necessity of obtaining explicit closures at
the macroscopic level. We also exploit the scheme to perform a rare-events
analysis by estimating an effective Fokker-Planck describing the evolving
probability density function of the corresponding coarse-grained observables
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