3,413 research outputs found
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
Pinning Complex Networks by a Single Controller
In this paper, without assuming symmetry, irreducibility, or linearity of the
couplings, we prove that a single controller can pin a coupled complex network
to a homogenous solution. Sufficient conditions are presented to guarantee the
convergence of the pinning process locally and globally. An effective approach
to adapt the coupling strength is proposed. Several numerical simulations are
given to verify our theoretical analysis
Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
A chimera state is a spatio-temporal pattern in a network of identical
coupled oscillators in which synchronous and asynchronous oscillation coexist.
This state of broken symmetry, which usually coexists with a stable spatially
symmetric state, has intrigued the nonlinear dynamics community since its
discovery in the early 2000s. Recent experiments have led to increasing
interest in the origin and dynamics of these states. Here we review the history
of research on chimera states and highlight major advances in understanding
their behaviour.Comment: 26 pages, 3 figure
Oscillatory phase transition and pulse propagation in noisy integrate-and-fire neurons
We study non-locally coupled noisy integrate-and-fire neurons with the
Fokker-Planck equation. A propagating pulse state and a wavy state appear as a
phase transition from an asynchronous state. We also find a solution in which
traveling pulses are emitted periodically from a pacemaker region.Comment: 9 pages, 4 figure
Emergence of multicluster chimera states
We thank Prof. L. Huang for helpful discussions. This work was partially supported by ARO under Grant No. W911NF-14-1-0504 and by NSF of China under Grant No. 11275003. The visit of NY to Arizona State University was partially sponsored by Prof. Z. Zheng and the State Scholarship Fund of China.Peer reviewedPublisher PD
Chimeras in Leaky Integrate-and-Fire Neural Networks: Effects of Reflecting Connectivities
The effects of nonlocal and reflecting connectivity are investigated in
coupled Leaky Integrate-and-Fire (LIF) elements, which assimilate the exchange
of electrical signals between neurons. Earlier investigations have demonstrated
that non-local and hierarchical network connectivity often induces complex
synchronization patterns and chimera states in systems of coupled oscillators.
In the LIF system we show that if the elements are non-locally linked with
positive diffusive coupling in a ring architecture the system splits into a
number of alternating domains. Half of these domains contain elements, whose
potential stays near the threshold, while they are interrupted by active
domains, where the elements perform regular LIF oscillations. The active
domains move around the ring with constant velocity, depending on the system
parameters. The idea of introducing reflecting non-local coupling in LIF
networks originates from signal exchange between neurons residing in the two
hemispheres in the brain. We show evidence that this connectivity induces novel
complex spatial and temporal structures: for relatively extensive ranges of
parameter values the system splits in two coexisting domains, one domain where
all elements stay near-threshold and one where incoherent states develop with
multileveled mean phase velocity distribution.Comment: 12 pages, 12 figure
Response of an Excitatory-Inhibitory Neural Network to External Stimulation: An Application to Image Segmentation
Neural network models comprising elements which have exclusively excitatory
or inhibitory synapses are capable of a wide range of dynamic behavior,
including chaos. In this paper, a simple excitatory-inhibitory neural pair,
which forms the building block of larger networks, is subjected to external
stimulation. The response shows transition between various types of dynamics,
depending upon the magnitude of the stimulus. Coupling such pairs over a local
neighborhood in a two-dimensional plane, the resultant network can achieve a
satisfactory segmentation of an image into ``object'' and ``background''.
Results for synthetic and and ``real-life'' images are given.Comment: 8 pages, latex, 5 figure
Describing synchronization and topological excitations in arrays of magnetic spin torque oscillators through the Kuramoto model
The collective dynamics in populations of magnetic spin torque oscillators
(STO) is an intensely studied topic in modern magnetism. Here, we show that
arrays of STO coupled via dipolar fields can be modeled using a variant of the
Kuramoto model, a well-known mathematical model in non-linear dynamics. By
investigating the collective dynamics in arrays of STO we find that the
synchronization in such systems is a finite size effect and show that the
critical coupling-for a complete synchronized state-scales with the number of
oscillators. Using realistic values of the dipolar coupling strength between
STO we show that this imposes an upper limit for the maximum number of
oscillators that can be synchronized. Further, we show that the lack of long
range order is associated with the formation of topological defects in the
phase field similar to the two-dimensional XY model of ferromagnetism. Our
results shed new light on the synchronization of STO, where controlling the
mutual synchronization of several oscillators is considered crucial for
applications.Comment: Accepted for publication in Scientific Reports. Corrected typo in
Eq.(9) from previous versio
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