1,263 research outputs found
Non-universal results induced by diversity distribution in coupled excitable systems
We consider a system of globally coupled active rotators near the excitable
regime. The system displays a transition to a state of collective firing
induced by disorder. We show that this transition is found generically for any
diversity distribution with well defined moments. Singularly, for the
Lorentzian distribution (widely used in Kuramoto-like systems) the transition
is not present. This warns about the use of Lorentzian distributions to
understand the generic properties of coupled oscillators
Multistable attractors in a network of phase oscillators with three-body interaction
Three-body interactions have been found in physics, biology, and sociology.
To investigate their effect on dynamical systems, as a first step, we study
numerically and theoretically a system of phase oscillators with three-body
interaction. As a result, an infinite number of multistable synchronized states
appear above a critical coupling strength, while a stable incoherent state
always exists for any coupling strength. Owing to the infinite multistability,
the degree of synchrony in asymptotic state can vary continuously within some
range depending on the initial phase pattern.Comment: 5 pages, 3 figure
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
Phaselocked patterns and amplitude death in a ring of delay coupled limit cycle oscillators
We study the existence and stability of phaselocked patterns and amplitude
death states in a closed chain of delay coupled identical limit cycle
oscillators that are near a supercritical Hopf bifurcation. The coupling is
limited to nearest neighbors and is linear. We analyze a model set of discrete
dynamical equations using the method of plane waves. The resultant dispersion
relation, which is valid for any arbitrary number of oscillators, displays
important differences from similar relations obtained from continuum models. We
discuss the general characteristics of the equilibrium states including their
dependencies on various system parameters. We next carry out a detailed linear
stability investigation of these states in order to delineate their actual
existence regions and to determine their parametric dependence on time delay.
Time delay is found to expand the range of possible phaselocked patterns and to
contribute favorably toward their stability. The amplitude death state is
studied in the parameter space of time delay and coupling strength. It is shown
that death island regions can exist for any number of oscillators N in the
presence of finite time delay. A particularly interesting result is that the
size of an island is independent of N when N is even but is a decreasing
function of N when N is odd.Comment: 23 pages, 12 figures (3 of the figures in PNG format, separately from
TeX); minor additions; typos correcte
Collective dynamical response of coupled oscillators with any network structure
We formulate a reduction theory that describes the response of an oscillator
network as a whole to external forcing applied nonuniformly to its constituent
oscillators. The phase description of multiple oscillator networks coupled
weakly is also developed. General formulae for the collective phase sensitivity
and the effective phase coupling between the oscillator networks are found. Our
theory is applicable to a wide variety of oscillator networks undergoing
frequency synchronization. Any network structure can systematically be treated.
A few examples are given to illustrate our theory.Comment: 4 pages, 2 figure
Interface instability in shear banding flow
We report on the spatio-temporal dynamics of the interface in shear-banding
flow of a wormlike micellar system (cetyltrimethylammonium bromide and sodium
nitrate in water) during a start-up experiment. Using the scattering properties
of the induced structures, we demonstrate the existence of an instability of
the interface between bands along the vorticity direction. Different regimes of
spatio-temporal dynamics of the interface are indentified along the stress
plateau. We build a model based on the flow symetry which qualitatively
describes the observed patterns
A power-law distribution of phase-locking intervals does not imply critical interaction
Neural synchronisation plays a critical role in information processing,
storage and transmission. Characterising the pattern of synchronisation is
therefore of great interest. It has recently been suggested that the brain
displays broadband criticality based on two measures of synchronisation - phase
locking intervals and global lability of synchronisation - showing power law
statistics at the critical threshold in a classical model of synchronisation.
In this paper, we provide evidence that, within the limits of the model
selection approach used to ascertain the presence of power law statistics, the
pooling of pairwise phase-locking intervals from a non-critically interacting
system can produce a distribution that is similarly assessed as being power
law. In contrast, the global lability of synchronisation measure is shown to
better discriminate critical from non critical interaction.Comment: (v3) Fixed error in Figure 1; (v2) Added references. Minor edits
throughout. Clarified relationship between theoretical critical coupling for
infinite size system and 'effective' critical coupling system for finite size
system. Improved presentation and discussion of results; results unchanged.
Revised Figure 1 to include error bars on r and N; results unchanged; (v1) 11
pages, 7 figure
Partially Solvable Anisotropic t-J Model with Long-Range Interactions
A new anisotropic t-J model in one dimension is proposed which has long-range
hopping and exchange. This t-J model is only partially solvable in contrast to
known integrable models with long-range interaction. In the high-density limit
the model reduces to the XXZ chain with the long-range exchange. Some exact
eigenfunctions are shown to be of Jastrow-type if certain conditions for an
anisotropy parameter are satisfied. The ground state as well as the excitation
spectrum for various cases of the anisotropy parameter and filling are derived
numerically. It is found that the Jastrow-type wave function is an excellent
trial function for any value of the anisotropy parameter.Comment: 10 pages, 3 Postscript figure
Multistable behavior above synchronization in a locally coupled Kuramoto model
A system of nearest neighbors Kuramoto-like coupled oscillators placed in a
ring is studied above the critical synchronization transition. We find a
richness of solutions when the coupling increases, which exists only within a
solvability region (SR). We also find that they posses different
characteristics, depending on the section of the boundary of the SR where the
solutions appear. We study the birth of these solutions and how they evolve
when {K} increases, and determine the diagram of solutions in phase space.Comment: 8 pages, 10 figure
Charge gaps and quasiparticle bands of the ionic Hubbard model
The ionic Hubbard model on a cubic lattice is investigated using analytical
approximations and Wilson's renormalization group for the charge excitation
spectrum. Near the Mott insulating regime, where the Hubbard repulsion starts
to dominate all energies, the formation of correlated bands is described. The
corresponding partial spectral weights and local densities of states show
characteristic features, which compare well with a hybridized-band picture
appropriate for the regime at small , which at half-filling is known as a
band insulator. In particular, a narrow charge gap is obtained at half-filling,
and the distribution of spectral quasi-particle weight reflects the fundamental
hybridization mechanism of the model
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