10 research outputs found
Recommended from our members
Optimal design of the tweezer control for chimera states
Chimera states are complex spatio-temporal patterns, which consist of
coexisting domains of spatially coherent and incoherent dynamics in systems
of coupled oscillators. In small networks, chimera states usually exhibit
short lifetimes and erratic drifting of the spatial position of the
incoherent domain. A tweezer feedback control scheme can stabilize and fix
the position of chimera states. We analyse the action of the tweezer control
in small nonlocally coupled networks of Van der Pol and FitzHugh-Nagumo
oscillators, and determine the ranges of optimal control parameters. We
demonstrate that the tweezer control scheme allows for stabilization of
chimera states with different shapes, and can be used as an instrument for
controlling the coherent domains size, as well as the maximum average
frequency difference of the oscillators
A Tweezer for Chimeras in Small Networks
We propose a control scheme which can stabilize and fix the position of
chimera states in small networks. Chimeras consist of coexisting domains of
spatially coherent and incoherent dynamics in systems of nonlocally coupled
identical oscillators. Chimera states are generally difficult to observe in
small networks due to their short lifetime and erratic drifting of the spatial
position of the incoherent domain. The control scheme, like a tweezer, might be
useful in experiments, where usually only small networks can be realized
Recommended from our members
Turbulence in the Ott-Antonsen equation for arrays of coupled phase oscillators
In this paper we study the transition to synchrony in an
one-dimensional array of oscillators with non-local coupling. For its
description in the continuum limit of a large number of phase oscillators, we
use a corresponding Ott-Antonsen equation, which is an integrodifferential
equation for the evolution of the macroscopic profiles of the local mean
field. Recently, it has been reported that in the spatially extended case at
the synchronization threshold there appear partially coherent plane waves
with different wave numbers, which are organized in the well-known Eckhaus
scenario. In this paper, we show that for Kuramoto-Sakaguchi phase
oscillators the phase lag parameter in the interaction function can induce a
Benjamin-Feir type instability of the partially coherent plane waves. The
emerging collective macroscopic chaos appears as an intermediate stage
between complete incoherence and stable partially coherent plane waves.We
give an analytic treatment of the Benjamin-Feir instability and its onset in
a codimension-two bifurcation in the Ott-Antonsen equation as well as a
numerical study of the transition from phase turbulence to amplitude
turbulence inside the Benjamin-Feir unstable region
Recommended from our members
The mathematics behind chimera states
Chimera states are self-organized spatiotemporal patterns of coexisting
coherence and incoherence. We give an overview of the main mathematical
methods used in studies of chimera states, focusing on chimera states in
spatially extended coupled oscillator systems. We discuss the continuum limit
approach to these states, Ott-Antonsen manifold reduction, finite size
chimera states, control of chimera states and the influence of system design
on the type of chimera state that is observed
Recommended from our members
A tweezer for chimeras in small networks
We propose a control scheme which can stabilize and fix the position of
chimera states in small networks. Chimeras consist of coexisting domains of
spatially coherent and incoherent dynamics in systems of nonlocally coupled
identical oscillators. Chimera states are generally difficult to observe in
small networks due to their short lifetime and erratic drifting of the
spatial position of the incoherent domain. The control scheme, like a
tweezer, might be useful in experiments, where usually only small networks
can be realized
Optimal design of tweezer control for chimera states
Chimera states are complex spatio-temporal patterns which consist of coexisting domains of spatially coherent and incoherent dynamics in systems of coupled oscillators. In small networks, chimera states usually exhibit short lifetimes and erratic drifting of the spatial position of the incoherent domain. A tweezer feedback control scheme can stabilize and fix the position of chimera states. We analyze the action of the tweezer control in small nonlocally coupled networks of Van der Pol and FitzHugh-Nagumo oscillators, and determine the ranges of optimal control parameters. We demonstrate that the tweezer control scheme allows for stabilization of chimera states with different shapes, and can be used as an instrument for controlling the coherent domains size, as well as the maximum average frequency difference of the oscillators
Recommended from our members
Surfing the edge: Finding nonlinear solutions using feedback control
Many transitional wall-bounded shear flows are characterised by the
coexistence in statespace of laminar and turbulent regimes. Probing the edge
boundary between the two attractors has led in the last decade to the
numerical discovery of new (unstable) solutions to the incompressible
Navier-Stokes equations. However, the iterative bisection method used to
achieve this can become prohibitively costly for large systems. Here we
suggest a simple feedback control strategy to stabilise edge states, hence
accelerating their numerical identification by several orders of magnitude.
The method is illustrated for several configurations of cylindrical pipe
flow. Travelling waves solutions are identified as edge states, and can be
isolated rapidly in only one short numerical run. A new branch of solutions
is also identified. When the edge state is a periodic orbit or chaotic state,
the feedback control does not converge precisely to solutions of the
uncontrolled system, but nevertheless brings the dynamics very close to the
original edge manifold in a single run. We discuss the opportunities offered
by the speed and simplicity of this new method to probe the structure of both
state space and parameter space