Results 1 to 10 of about 5,047,277 (293)
Exponential attractors for random dynamical systems and applications [PDF]
arXiv, 2012 The paper is devoted to constructing a random exponential attractor for some classes of stochastic PDE's. We first prove the existence of an exponential attractor for abstract random dynamical systems and study its dependence on a parameter and then apply these results to a nonlinear reaction-diffusion system with a random perturbation.
Shirikyan, Armen, Zelik, Sergey
arxiv +15 more sources
Analysis of attractor distances in Random Boolean Networks [PDF]
arXiv, 2010 We study the properties of the distance between attractors in Random Boolean Networks, a prominent model of genetic regulatory networks. We define three distance measures, upon which attractor distance matrices are constructed and their main statistic parameters are computed.
Benedettini, Stefano +3 more
arxiv +4 more sources
Flattening, squeezing and the existence of random attractors [PDF]
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2006 The study of qualitative properties of random and stochastic differential equations is now one of the most active fields in the modern theory of dynamical systems. In the deterministic case, the properties of flattening and squeezing in infinite-dimensional autonomous dynamical systems require the existence of a bounded absorbing set and imply the ...
Peter E. Kloeden, José A. Langa
openalex +4 more sources
Random maps and attractors in random Boolean networks [PDF]
Physical Review E, 2005 Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. The topologies of random Boolean networks with one input per node can be seen as graphs of random maps.
Carl Troein, Björn Samuelsson
arxiv +6 more sources
Random Attractors for the Stochastic Benjamin-Bona-Mahony Equation on Unbounded Domains [PDF]
arXiv, 2008 We prove the existence of a compact random attractor for the stochastic Benjamin-Bona-Mahony Equation defined on an unbounded domain. This random attractor is invariant and attracts every pulled-back tempered random set under the forward flow. The asymptotic compactness of the random dynamical system is established by a tail-estimates method, which ...
Wang, Bixiang
arxiv +4 more sources
Criteria for strong and weak random attractors [PDF]
J. Dynam. Differential Equations 21 (2009) no. 2, 233-247, 2008 The theory of random attractors has different notions of attraction, amongst them pullback attraction and weak attraction. We investigate necessary and sufficient conditions for the existence of pullback attractors as well as of weak attractors.
Georgi Dimitroff +2 more
arxiv +6 more sources
Connectedness of random set attractors [PDF]
arXiv, 2017 We examine the question whether random set attractors for continuous-time random dynamical systems on a connected state space are connected. In the deterministic case, these attractors are known to be connected. In the probabilistic setup, however, connectedness has only been shown under stronger connectedness assumptions on the state space.
Scheutzow, Michael, Vorkastner, Isabell
arxiv +5 more sources
Global attractors for multivalued random dynamical systems [PDF]
Nonlinear Analysis: Theory, Methods & Applications, 2002 We introduce the concept of multivalued random dynamical system (MRDS) as a measurable multivalued flow satisfying the cocycle property. We show how this is a suitable framework for the study of the asymptotic behaviour of some multivalued stochastic parabolic equations by generalizing the concept of global random attractor to the case of a MRDS.
Tomás Caraballo +2 more
openalex +4 more sources
Properties of attractors of canalyzing random Boolean networks [PDF]
Physical Review E, 2006 9 pages, 8 ...
Utpal Kumar Paul +2 more
openalex +6 more sources
The asymptotic number of attractors in the random map model [PDF]
Journal of Physics A: Mathematical and General, 2003 The random map model is a deterministic dynamical system in a finite phase space with n points. The map that establishes the dynamics of the system is constructed by randomly choosing, for every point, another one as being its image. We derive here explicit formulas for the statistical distribution of the number of attractors in the system.
David Romero, Federico Zertuche
openalex +4 more sources