117 research outputs found
Basins of Attraction for Chimera States
Chimera states---curious symmetry-broken states in systems of identical
coupled oscillators---typically occur only for certain initial conditions. Here
we analyze their basins of attraction in a simple system comprised of two
populations. Using perturbative analysis and numerical simulation we evaluate
asymptotic states and associated destination maps, and demonstrate that basins
form a complex twisting structure in phase space. Understanding the basins'
precise nature may help in the development of control methods to switch between
chimera patterns, with possible technological and neural system applications.Comment: Please see Ancillary files for the 4 supplementary videos including
description (PDF
Asymmetry--induced effects in coupled phase oscillator ensembles: Routes to synchronization
A system of two coupled ensembles of phase oscillators can follow different
routes to inter-ensemble synchronization. Following a short report of our
preliminary results [Phys. Rev. E. {\bf 78}, 025201(R) (2008)], we present a
more detailed study of the effects of coupling, noise and phase asymmetries in
coupled phase oscillator ensembles. We identify five distinct synchronization
regions, and new routes to synchronization that are characteristic of the
coupling asymmetry. We show that noise asymmetry induces effects similar to
that of coupling asymmetry when the latter is absent. We also find that phase
asymmetry controls the probability of occurrence of particular routes to
synchronization. Our results suggest that asymmetry plays a crucial role in
controlling synchronization within and between oscillator ensembles, and hence
that its consideration is vital for modeling real life problems
Collective power: Minimal model for thermodynamics of nonequilibrium phase transitions
We propose a thermodynamically consistent minimal model to study
synchronization which is made of driven and interacting three-state units. This
system exhibits at the mean-field level two bifurcations separating three
dynamical phases: a single stable fixed point, a stable limit cycle indicative
of synchronization, and multiple stable fixed points. These complex emergent
dynamical behaviors are understood at the level of the underlying linear
Markovian dynamics in terms of metastability, i.e. the appearance of gaps in
the upper real part of the spectrum of the Markov generator. Stochastic
thermodynamics is used to study the dissipated work across dynamical phases as
well as across scales. This dissipated work is found to be reduced by the
attractive interactions between the units and to nontrivially depend on the
system size. When operating as a work-to-work converter, we find that the
maximum power output is achieved far-from-equilibrium in the synchronization
regime and that the efficiency at maximum power is surprisingly close to the
linear regime prediction. Our work shows the way towards building a
thermodynamics of nonequilibrium phase transitions in conjunction to
bifurcation theory.Comment: 20 pages, 12 figure
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