共查询到20条相似文献,搜索用时 15 毫秒
1.
Mitchell J. Feigenbaum 《Journal of statistical physics》1987,46(5-6):925-932
The grand canonical version of the spectrum of singularities formalism is presented, relying naturally upon certain Markov transition graphs. The structure of a graph is simply determined by the close return times of the dynamical system described. Thus, an intimate connection exists between the shape of the singularity curve and a small but interesting set of dynamical properties. 相似文献
2.
Michihiro Hirayama 《Journal of statistical physics》2005,118(1-2):103-118
Consider basic set for Axiom A diffeomorphism on compact surface.We derive second variational formulae for the dimension spectra of equilibrium state on the basic set with respect to the perturbations of both the potential and\break the dynamical system.In particular we obtain a second variational formula for the Hausdorff dimension of the basic set.These results will find their use in the study of a quadratic extremal problem for multifrcatal analysis. 相似文献
3.
Mitchell J. Feigenbaum 《Journal of statistical physics》1987,46(5-6):919-924
A thermodynamic formalism is exhibited that is the canonical version of Halseyet al.'s microcanonical formulation. This formalism is applied to a four-scale Cantor set and it is shown that the singularity spectrum fails to uniquely encode the underlying dynamics. 相似文献
4.
V. Baladi 《Journal of statistical physics》1991,62(1-2):239-256
We studyfinitely presented dynamical systems (which generalize Axiom A systems) and show that the notions of equilibrium states and Gibbs states (for Hölder continuous functions) are equivalent. Our results extend those of Ruelle, Haydn, and others on Axiom A dynamical systems and statistical mechanics. 相似文献
5.
6.
David Ruelle 《Communications in Mathematical Physics》1996,175(1):63-88
A Milnor-Thurston type dynamical zeta function
L
(Z) is associated with a family of maps of the interval (–1, 1). Changing the direction of time produces a new zeta function
L
(Z). These zeta functions satisfy a functional equation
L
(Z)
L
(Z)=
0(Z) (where amounts to sign changes and, generically,01). The functional equation has non-trivial implications for the analytic properties of
L
(Z). 相似文献
7.
8.
Differential equations and maps are the most frequently studied examples of dynamical systems and may be considered as continuous
and discrete time-evolution processes respectively. The processes in which time evolution takes place on Cantor-like fractal
subsets of the real line may be termed as fractal-time dynamical systems. Formulation of these systems requires an appropriate
framework. A new calculus calledF
α-calculus, is a natural calculus on subsetsF⊂ R of dimension α,0 < α ≤ 1. It involves integral and derivative of order α, calledF
α-integral andF
α-derivative respectively. TheF
α-integral is suitable for integrating functions with fractal support of dimension α, while theF
α-derivative enables us to differentiate functions like the Cantor staircase. The functions like the Cantor staircase function
occur naturally as solutions ofF
α-differential equations. Hence the latter can be used to model fractal-time processes or sublinear dynamical systems.
We discuss construction and solutions of some fractal differential equations of the form
whereh is a vector field andD
F,t
α
is a fractal differential operator of order α in timet. We also consider some equations of the form
whereL is an ordinary differential operator in the real variablex, and(t,x) ∈F × Rn whereF is a Cantor-like set of dimension α.
Further, we discuss a method of finding solutions toF
α-differential equations: They can be mapped to ordinary differential equations, and the solutions of the latter can be transformed
back to get those of the former. This is illustrated with a couple of examples. 相似文献
9.
Miaohua Jiang 《Journal of statistical physics》2003,111(3-4):863-902
For weakly coupled expanding maps on the unit circle, Bricmont and Kupiainen showed that the Sinai-Ruelle-Bowen (SRB) measure exists as a Gibbs state. Via thermodynamic formalism, we prove that this SRB measure is indeed the unique equilibrium state for a Hölder continuous potential function on the infinite dimensional phase space. For a more general class of lattice systems that are small perturbations of the uncoupled map lattice, we present the variational principle, the entropy formula, and the formula for the potential function for the SRB measures. For coupled map lattices with nearest neighbor interactions, we give an explicit formula of the potential function for the SRB measure and consequently, obtain the entropy in terms of coupling parameters. 相似文献
10.
A cellular-automaton-like caricature of chemical turbulence on an infinite one-dimensional lattice is studied. The model exhibits apparently turbulent space-time patterns. To make this statement precise, the following problems or points are discussed: (1) The infinite-system-size limit of such cell-dynamical systems and its observability is defined. (2) It is proved that the invariant state in the large-system-size limit of the turbulent phase exhibits spatial patterns governed by a Gibbs random field. (3) Potential characteristics of turbulent space-time patterns are critically surveyed and a working definition of (weak) turbulence is proposed. (4) It is proved that the invariant state of the turbulent phase is actually (weak) turbulent. Furthermore, we conjecture that the turbulent phase of our model is an example of a K system that is not Bernoulli. 相似文献
11.
We study a discrete dynamical system whose evolution is governed by rules similar to those of Conway's game of Life but also include a stochastic element (parametrized by a temperature). Statistical properties that are examined are density as a function of temperature and entropy (suitably defined). A phase transition and a certain thermodynamic constant of the motion are observed.Lady Davis Visiting Scientist at the Technion 1974–75. 相似文献
12.
13.
A mechanism is suggested to explain the information processing abilities of simple natural brains, which, by experimental evidence, display behavior like chaotic dynamical systems while at rest. The Lorenz system of equations is dealt with as a case study, and a comparison of the suggested mechanism with the standard theory of neural networks is made. 相似文献
14.
We construct new unidirectional coupling schemes for autonomous and nonautonomous drive systems, respectively. Each of these schemes makes the state of the response system asymptotically approach the first-order derivative of the state of the driver. From the point of view of geometry, the first-order derivative of the state of the driver can be viewed as a tangent vector of the trajectory of the driver, so the proposed schemes are named tangent response schemes. Numerical simulations of the Lorenz system and the forced Duffing oscillator verify the validity of the tangent response schemes. We further point out that the tangent response can be interpreted as a special kind of generalised synchronisation, thereby explaining why the response system can exhibit rich geometrical structures in its state space. 相似文献
15.
In this Letter, we investigate the problem of impulsive synchronization of networked multi-agent systems, where each agent can be modeled as an identical nonlinear dynamical system. Firstly, an impulsive control protocol is designed for network with fixed topology based on the local information of agents. Then sufficient conditions are given to guarantee the synchronization of the networked nonlinear dynamical system by using algebraic graph theory and impulsive control theory. Furthermore, how to select the discrete instants and impulsive constants is discussed. The case that the topologies of the networks are switching is also considered. Numerical simulations show the effectiveness of our theoretical results. 相似文献
16.
A.J. Roberts 《Physica A》2008,387(1):12-38
Modelling stochastic systems has many important applications. Normal form coordinate transforms are a powerful way to untangle interesting long term macroscale dynamics from insignificant detailed microscale dynamics. We explore such coordinate transforms of stochastic differential systems when the dynamics have both slow modes and quickly decaying modes. The thrust is to derive normal forms useful for macroscopic modelling of complex stochastic microscopic systems. Thus we not only must reduce the dimensionality of the dynamics, but also endeavour to separate all slow processes from all fast time processes, both deterministic and stochastic. Quadratic stochastic effects in the fast modes contribute to the drift of the important slow modes. Some examples demonstrate that the coordinate transform may be only locally valid or may be globally valid depending upon the dynamical system. The results will help us accurately model, interpret and simulate multiscale stochastic systems. 相似文献
17.
G. Grinstein 《Journal of statistical physics》1988,51(5-6):803-815
We summarize recent arguments which show that for a broad class of classical, many-body dynamical model systems with short-range interactions (such as coupled maps, cellular automata, or partial differential equations), collectively chaotic states—nonstationary states wherein some Fourier amplitude varies chaotically in time—cannot occur generically. While chaos occurs ubiquitously on alocal level in such systems, the macroscopic state of the system typically remains periodic or stationary. This implies that the dimensionD of chaotic (strange) attractors must diverge with the linear sizeL of the system likeD(L/C)d ind space dimensions, where (<) is the spatial coherence length. We also summarize recent work which demonstrates that in spatially isotropic systems that have short-range interactions and evolve (like coupled maps) in discrete time, periodic states are never stable under generic conditions. In spatially anisotropic systems, however, short-range interactions that exploit the anisotropy and so allow for the stabilization of periodic states do exist. 相似文献
18.
19.
Sanjay Puri 《Pramana》1997,48(2):737-748
We study experimentally relevant effects in phase ordering dynamics using Cell Dynamical System (CDS) models. In particular,
we present representative numerical results for phase ordering in random magnets and phase separation in binary fluids. 相似文献
20.
Nonequilibrium molecular dynamics simulations are used to demonstrate the asymptotic convergence of the transient and steady-state forms of the fluctuation theorem. In the case of planar Poiseuille flow, we find that the transient form, valid for all times, converges to the steady-state predictions on microscopic time scales. Further, we find that the time of convergence for the two theorems coincides with the time required for satisfaction of the asymptotic steady-state fluctuation theorem. 相似文献