1,650 research outputs found
Synchronous solutions and their stability in nonlocally coupled phase oscillators with propagation delays
We study the existence and stability of synchronous solutions in a continuum
field of non-locally coupled identical phase oscillators with
distance-dependent propagation delays. We present a comprehensive stability
diagram in the parameter space of the system. From the numerical results a
heuristic synchronization condition is suggested, and an analytic relation for
the marginal stability curve is obtained. We also provide an expression in the
form of a scaling relation that closely follows the marginal stability curve
over the complete range of the non-locality parameter.Comment: accepted in Phys. Rev. E (2010
Swarm-Oscillators
Nonlinear coupling between inter- and intra-element dynamics appears as a
collective behaviour of elements. The elements in this paper denote symptoms
such as a bacterium having an internal network of genes and proteins, a
reactive droplet, a neuron in networks, etc. In order to elucidate the
capability of such systems, a simple and reasonable model is derived. This
model exhibits the rich patterns of systems such as cell membrane, cell fusion,
cell growing, cell division, firework, branch, and clustered clusters
(self-organized hierarchical structure, modular network). This model is
extremely simple yet powerful; therefore, it is expected to impact several
disciplines.Comment: 9 pages, 4 figure
Chimera Ising Walls in Forced Nonlocally Coupled Oscillators
Nonlocally coupled oscillator systems can exhibit an exotic spatiotemporal
structure called chimera, where the system splits into two groups of
oscillators with sharp boundaries, one of which is phase-locked and the other
is phase-randomized. Two examples of the chimera states are known: the first
one appears in a ring of phase oscillators, and the second one is associated
with the two-dimensional rotating spiral waves. In this article, we report yet
another example of the chimera state that is associated with the so-called
Ising walls in one-dimensional spatially extended systems, which is exhibited
by a nonlocally coupled complex Ginzburg-Landau equation with external forcing.Comment: 7 pages, 5 figures, to appear in Phys. Rev.
Hole Structures in Nonlocally Coupled Noisy Phase Oscillators
We demonstrate that a system of nonlocally coupled noisy phase oscillators
can collectively exhibit a hole structure, which manifests itself in the
spatial phase distribution of the oscillators. The phase model is described by
a nonlinear Fokker-Planck equation, which can be reduced to the complex
Ginzburg-Landau equation near the Hopf bifurcation point of the uniform
solution. By numerical simulations, we show that the hole structure clearly
appears in the space-dependent order parameter, which corresponds to the
Nozaki-Bekki hole solution of the complex Ginzburg-Landau equation.Comment: 4 pages, 4 figures, to appear in Phys. Rev.
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
Collective Phase Sensitivity
The collective phase response to a macroscopic external perturbation of a
population of interacting nonlinear elements exhibiting collective oscillations
is formulated for the case of globally-coupled oscillators. The macroscopic
phase sensitivity is derived from the microscopic phase sensitivity of the
constituent oscillators by a two-step phase reduction. We apply this result to
quantify the stability of the macroscopic common-noise induced synchronization
of two uncoupled populations of oscillators undergoing coherent collective
oscillations.Comment: 6 pages, 3 figure
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
The Kuramoto model with distributed shear
We uncover a solvable generalization of the Kuramoto model in which shears
(or nonisochronicities) and natural frequencies are distributed and
statistically dependent. We show that the strength and sign of this dependence
greatly alter synchronization and yield qualitatively different phase diagrams.
The Ott-Antonsen ansatz allows us to obtain analytical results for a specific
family of joint distributions. We also derive, using linear stability analysis,
general formulae for the stability border of incoherence.Comment: 6 page
Paths to Synchronization on Complex Networks
The understanding of emergent collective phenomena in natural and social
systems has driven the interest of scientists from different disciplines during
decades. Among these phenomena, the synchronization of a set of interacting
individuals or units has been intensively studied because of its ubiquity in
the natural world. In this paper, we show how for fixed coupling strengths
local patterns of synchronization emerge differently in homogeneous and
heterogeneous complex networks, driving the process towards a certain global
synchronization degree following different paths. The dependence of the
dynamics on the coupling strength and on the topology is unveiled. This study
provides a new perspective and tools to understand this emerging phenomena.Comment: Final version published in Physical Review Letter
Shear diversity prevents collective synchronization
Large ensembles of heterogeneous oscillators often exhibit collective
synchronization as a result of mutual interactions. If the oscillators have
distributed natural frequencies and common shear (or nonisochronicity), the
transition from incoherence to collective synchronization is known to occur at
large enough values of the coupling strength. However, here we demonstrate that
shear diversity cannot be counterbalanced by diffusive coupling leading to
synchronization. We present the first analytical results for the Kuramoto model
with distributed shear, and show that the onset of collective synchronization
is impossible if the width of the shear distribution exceeds a precise
threshold
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