Search PubMed⌕ Search
Home/Archive/PubMed

PubMed · 15244911

Random Boolean network model exhibiting deterministic chaos.

Mihaela T Matache·Jack Heidel
View original source ↗Export metadata ↓

Abstract

This paper considers a simple Boolean network with N nodes, each node's state at time t being determined by a certain number of parent nodes, which may vary from one node to another. This is an extension of a model studied by Andrecut and Ali [Int. J. Mod. Phys. B 15, 17 (2001)]], who consider the same number of parents for all nodes. We make use of the same Boolean rule as Andrecut and Ali, provide a generalization of the formula for the probability of finding a node in state 1 at a time t, and use simulation methods to generate consecutive states of the network for both the real system and the model. The results match well. We study the dynamics of the model through sensitivity of the orbits to initial values, bifurcation diagrams, and fixed point analysis. We show that the route to chaos is due to a cascade of period-doubling bifurcations which turn into reversed (period-halving) bifurcations for certain combinations of parameter values.

Explore related subjects

BiophysicsModels, StatisticalModels, TheoreticalNonlinear DynamicsTime FactorsJournal ArticleResearch Support, U.S. Gov't, P.H.S.

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Mihaela T Matache, Jack Heidel. 2004-05-19. Random Boolean network model exhibiting deterministic chaos.. https://doi.org/10.1103/physreve.69.056214

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related citations

PubMed2004

Raman spectroscopy of graphite.

We present a review of the Raman spectra of graphite from an experimental and theoretical point of view. The disorder-induced Raman bands in this material have been a puzzling Raman problem for almost 30 years. Double-resonant Raman scattering explains their origin as well as the excitation-energy dependence, the overtone spectrum and the difference between Stokes and anti-Stokes scattering. We develop the symmetry-imposed selection rules for double-resonant Raman scattering in graphite and point out misassignments in previously published works. An excellent agreement is found between the graphite phonon dispersion from double-resonant Raman scattering and other experimental methods.

Biophysics↗
PubMed2004

A wake-up call.

Explore the source record for details and available documents.

Biophysics↗
PubMed2004

Protein folding in high-dimensional spaces: hypergutters and the role of nonnative interactions.

We explore the consequences of very high dimensionality in the dynamical landscape of protein folding. Consideration of both typical range of stabilizing interactions, and folding rates themselves, leads to a model of the energy hypersurface that is characterized by the structure of diffusive "hypergutters" as well as the familiar "funnels". Several general predictions result: 1), intermediate subspaces of configurations will always be visited; 2), specific but nonnative interactions may be important in stabilizing these low-dimensional diffusive searches on the folding pathway, as well as native interactions; 3), sequential barriers will commonly be found, even in "two-state" proteins; 4), very early times will show characteristic departures from single-exponential kinetics; and 5), contributions of nonnative interactions to Phi-values and "Chevron plots" are calculable, and may be significant. The example of a three-helix bundle is treated in more detail as an illustration. The model also shows that high-dimensional structures provide conceptual relations between different models of protein folding. It suggests that kinetic strategies for fast folding may be encoded rather generally in nonnative as well as in native interactions. The predictions are related to very recent findings in experiment and simulation.

Biophysics↗