TITLE

Criticality in conserved dynamical systems: Experimental observation vs. exact properties

AUTHOR(S)
Markovic, Dimitrije; Gros, Claudius; Schuelein, André
PUB. DATE
March 2013
SOURCE
Chaos;Mar2013, Vol. 23 Issue 1, p013106
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Conserved dynamical systems are generally considered to be critical. We study a class of critical routing models, equivalent to random maps, which can be solved rigorously in the thermodynamic limit. The information flow is conserved for these routing models and governed by cyclic attractors. We consider two classes of information flow, Markovian routing without memory and vertex routing involving a one-step routing memory. Investigating the respective cycle length distributions for complete graphs, we find log corrections to power-law scaling for the mean cycle length, as a function of the number of vertices, and a sub-polynomial growth for the overall number of cycles. When observing experimentally a real-world dynamical system one normally samples stochastically its phase space. The number and the length of the attractors are then weighted by the size of their respective basins of attraction. This situation is equivalent, for theory studies, to 'on the fly' generation of the dynamical transition probabilities. For the case of vertex routing models, we find in this case power law scaling for the weighted average length of attractors, for both conserved routing models. These results show that the critical dynamical systems are generically not scale-invariant but may show power-law scaling when sampled stochastically. It is hence important to distinguish between intrinsic properties of a critical dynamical system and its behavior that one would observe when randomly probing its phase space.
ACCESSION #
86446937

 

Related Articles

  • Loss of Temporal Homogeneity and Symmetry in Statistical Systems: Deterministic Versus Stochastic Dynamics. Gujrati, Purushottam D. // Symmetry (20738994);Sep2010, Vol. 2 Issue 3, p1201 

    A detailed analysis of deterministic (one-to-one) and stochastic (one-to-many) dynamics establishes that dS/dt > 0 is only consistent with the latter, which contains violation of temporal symmetry and homogeneity. We observe that the former only supports dS/dt = 0 and cannot give rise to...

  • Different Methods of Partitioning the Phase Space of a Dynamic System. Hadriche, Abir; Jmail, Nawel; Elleuch, Ridha // International Journal of Computer Applications;May2014, Vol. 93, p1 

    In the symbolic dynamic, the principal problem to define a symbolic sequence of temporel time series is the use of an appropriate partition of the phase space trajectory data set. In fact, The best way is to estimate the generating partition. However, it is not possible to find generating...

  • Efficient determination of thermodynamic properties from a single simulation. Rickman, J. M.; Srolovitz, D. J. // Journal of Chemical Physics;11/15/1993, Vol. 99 Issue 10, p7993 

    A method for calculating the density of states of a system directly from its trajectory in phase space is described. As a specific example, the method is applied to the Monte Carlo simulation of a two-dimensional Ising model. The energy distribution function is calculated from the density of...

  • An alternate characterization of integrability. Das, Ashok; Huang, Wen-Jui // Journal of Mathematical Physics;Nov90, Vol. 31 Issue 11, p2603 

    This paper will show that the existence of at least three independent symplectic forms (related in a simple way) on the phase space of a dynamical system is a sufficient condition for the integrability of the system.

  • Fractal dimension of steady nonequilibrium flows. Hoover, William G.; Posch, Harald A. // Chaos;Apr92, Vol. 2 Issue 2, p245 

    Evaluates the Kaplan-Yorke information dimension of phase-space attractors for two kinds of steady nonequilibrium many-body flows. Consideration of a set of Newtonian particles which interacts with boundary particles; Imposition of time-averaged boundary temperatures by Nose-Hoover thermostat...

  • Information entropy production in non-Markovian systems. Bag, Bidhan Chandra // Journal of Chemical Physics;9/1/2003, Vol. 119 Issue 9, p4988 

    In this paper we have calculated the information entropy production along with the entropy flux in the nonequilibrium and equilibrium states for the non-Markovian systems using the Fokker–Planck and the entropy balance equations. © 2003 American Institute of Physics.

  • Microcanonical Monte Carlo simulation of thermodynamic properties. Lustig, Rolf // Journal of Chemical Physics;11/22/1998, Vol. 109 Issue 20, p8816 

    Investigates the Monte Carlo simulation of thermodynamic properties in the microcanonical ensemble. Reliability and accuracy of the Monte Carlo method; Prediction of bulk properties under periodic boundary conditions; Results of the transformation of a molecular system classical phase space...

  • Topological Classification of Limit Cycles of Piecewise Smooth Dynamical Systems and Its Associated Non-Standard Bifurcations. Taborda, John Alexander; Arango, Ivan // Entropy;Apr2014, Vol. 16 Issue 4, p1949 

    In this paper, we propose a novel strategy for the synthesis and the classification of nonsmooth limit cycles and its bifurcations (named Non-Standard Bifurcations or Discontinuity Induced Bifurcations or DIBs) in n-dimensional piecewise-smooth dynamical systems, particularly Continuous PWS and...

  • Detection of Nonlinearity and Stochastic Nature in Time Series by Delay Vector Variance Method. Ahmed, Imtiaz // International Journal of Engineering & Technology;Apr2010, Vol. 10 Issue 2, p22 

    This paper investigates the suitability of Delay Vector Variance (DVV) algorithm in determining the presence of nonlinear and stochastic nature of time series both in the presence and absence of chaos. A differential entropy based method is used to find the optimum embedding dimension and time...

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics