4,546 research outputs found
Attractors for non-autonomous retarded lattice dynamical systems
In this paperwe study a non-autonomous lattice dynamical system with delay. Under rather general growth and dissipative conditions on the nonlinear term,we define a non-autonomous dynamical system and prove the existence of a pullback attractor for such system as well. Both multivalued and single-valued cases are considered
Existence of random attractors for a class of second order lattice dynamical systems with Brownian motions
Copyright © 2014 Yamin Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.For abstract, see attached file.The National Natural Science Foundation of China under Grant nos. 61374010, 61074129, and 61175111, the Natural Science Foundation of Jiangsu Province of China under Grant BK2012682, the Qing
Lan Project of Jiangsu Province (2010), the 333 Project of Jiangsu Province (2011), and the Six Talents Peak Project of Jiangsu Province (DZXX-047)
Continuation Sheaves in Dynamics: Sheaf Cohomology and Bifurcation
Continuation of algebraic structures in families of dynamical systems is
described using category theory, sheaves, and lattice algebras. Well-known
concepts in dynamics, such as attractors or invariant sets, are formulated as
functors on appropriate categories of dynamical systems mapping to categories
of lattices, posets, rings or abelian groups. Sheaves are constructed from such
functors, which encode data about the continuation of structure as system
parameters vary. Similarly, morphisms for the sheaves in question arise from
natural transformations. This framework is applied to a variety of lattice
algebras and ring structures associated to dynamical systems, whose algebraic
properties carry over to their respective sheaves. Furthermore, the cohomology
of these sheaves are algebraic invariants which contain information about
bifurcations of the parametrized systems
Metastability in zero-temperature dynamics: Statistics of attractors
The zero-temperature dynamics of simple models such as Ising ferromagnets
provides, as an alternative to the mean-field situation, interesting examples
of dynamical systems with many attractors (absorbing configurations, blocked
configurations, zero-temperature metastable states). After a brief review of
metastability in the mean-field ferromagnet and of the droplet picture, we
focus our attention onto zero-temperature single-spin-flip dynamics of
ferromagnetic Ising models. The situations leading to metastability are
characterized. The statistics and the spatial structure of the attractors thus
obtained are investigated, and put in perspective with uniform a priori
ensembles. We review the vast amount of exact results available in one
dimension, and present original results on the square and honeycomb lattices.Comment: 21 pages, 6 figures. To appear in special issue of JPCM on Granular
Matter edited by M. Nicodem
Relation between coupled map lattices and kinetic Ising models
A spatially one dimensional coupled map lattice possessing the same
symmetries as the Miller Huse model is introduced. Our model is studied
analytically by means of a formal perturbation expansion which uses weak
coupling and the vicinity to a symmetry breaking bifurcation point. In
parameter space four phases with different ergodic behaviour are observed.
Although the coupling in the map lattice is diffusive, antiferromagnetic
ordering is predominant. Via coarse graining the deterministic model is mapped
to a master equation which establishes an equivalence between our system and a
kinetic Ising model. Such an approach sheds some light on the dependence of the
transient behaviour on the system size and the nature of the phase transitions.Comment: 15 pages, figures included, Phys. Rev. E in pres
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