1,457 research outputs found
Spreading in Disordered Lattices with Different Nonlinearities
We study the spreading of initially localized states in a nonlinear
disordered lattice described by the nonlinear Schr\"odinger equation with
random on-site potentials - a nonlinear generalization of the Anderson model of
localization. We use a nonlinear diffusion equation to describe the
subdiffusive spreading. To confirm the self-similar nature of the evolution we
characterize the peak structure of the spreading states with help of R\'enyi
entropies and in particular with the structural entropy. The latter is shown to
remain constant over a wide range of time. Furthermore, we report on the
dependence of the spreading exponents on the nonlinearity index in the
generalized nonlinear Schr\"odinger disordered lattice, and show that these
quantities are in accordance with previous theoretical estimates, based on
assumptions of weak and very weak chaoticity of the dynamics.Comment: 5 pages, 6 figure
Mode-locking and mode-competition in a non-equilibrium solid-state condensate
A trapped polariton condensate with continuous pumping and decay is analyzed
using a generalized Gross-Pitaevskii model. Whereas an equilibrium condensate
is characterized by a macroscopic occupation of a ground state, here the
steady-states take more general forms. Some are characterized by a large
population in an excited state, and others by large populations in several
states. In the latter case, the highly-populated states synchronize to a common
frequency above a critical density. Estimates for the critical density of this
synchronization transition are consistent with experiments.Comment: 5 pages, 2 figure
Phase synchronization in time-delay systems
Though the notion of phase synchronization has been well studied in chaotic
dynamical systems without delay, it has not been realized yet in chaotic
time-delay systems exhibiting non-phase coherent hyperchaotic attractors. In
this article we report the first identification of phase synchronization in
coupled time-delay systems exhibiting hyperchaotic attractor. We show that
there is a transition from non-synchronized behavior to phase and then to
generalized synchronization as a function of coupling strength. These
transitions are characterized by recurrence quantification analysis, by phase
differences based on a new transformation of the attractors and also by the
changes in the Lyapunov exponents. We have found these transitions in coupled
piece-wise linear and in Mackey-Glass time-delay systems.Comment: 4 pages, 3 Figures (To appear in Physical Review E Rapid
Communication
Dynamics of multi-frequency oscillator ensembles with resonant coupling
We study dynamics of populations of resonantly coupled oscillators having
different frequencies. Starting from the coupled van der Pol equations we
derive the Kuramoto-type phase model for the situation, where the natural
frequencies of two interacting subpopulations are in relation 2:1. Depending on
the parameter of coupling, ensembles can demonstrate fully synchronous
clusters, partial synchrony (only one subpopulation synchronizes), or
asynchrony in both subpopulations. Theoretical description of the dynamics
based on the Watanabe-Strogatz approach is developed.Comment: 12 page
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