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Chaotic Dynamics papers — page 18

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Behavior of the Dripping Faucet over a Wide Range of the Flow Rate
The time interval of successive water-drips from a faucet was examined over a wide range of the flow rate. The dripping interval alternately exhibits a stable state and a chaotic state as the flow…
Tomoo Katsuyama, Ken-ichi NagataJan 18, 1999
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Characterization and control of small-world networks
Recently Watts and Strogatz have given an interesting model of small-world networks. Here we concretise the concept of a ``far away'' connection in a network by defining a far edge. Our…
S. A. Pandit, R. E. AmritkarJan 16, 1999
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Analytic estimate of the maximum Lyapunov exponent in coupled-map lattices
In this work we present a theoretical and numerical study of the behaviour of the maximum Lyapunov exponent for a generic coupled-map-lattice in the weak-coupling regime. We explain the observed…
F. Cecconi, A. PolitiJan 13, 1999
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The predictability problem in systems with an uncertainty in the evolution law
The problem of error growth due to the incomplete knowledge of the evolution law which rules the dynamics of a given physical system is addressed. Major interest is devoted to the analysis of error…
G. Boffetta, A. Celani, M. Cencini et al.Jan 13, 1999
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Advection-dispersion in symmetric field-flow fractionation channels
We model the evolution of the concentration field of macromolecules in a symmetric field-flow fractionation (FFF) channel by a one-dimensional advection-diffusion equation. The coefficients are…
S. A. Suslov, A. J. RobertsJan 13, 1999
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Holistic finite differences ensure fidelity to Burger's equation
I analyse a generalised Burger's equation to develop an accurate finite difference approximation to its dynamics. The analysis is based upon centre manifold theory so we are assured that the…
A. J. RobertsJan 13, 1999
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Computer algebra derives correct initial conditions for low-dimensional dynamical models
To ease analysis and simulation we make low-dimensional models of complicated dynamical systems. Centre manifold theory provides a systematic basis for the reduction of dimensionality from some…
A. J. RobertsJan 13, 1999
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Scaling and Intermittency in Animal Behavior
Scale-invariant spatial or temporal patterns and Lévy flight motion have been observed in a large variety of biological systems. It has been argued that animals in general might perform Lévy flight…
A. Harnos, G. Horvath, A. B. Lawrence et al.Jan 12, 1999
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Chaos in monopole sector of the Georgi-Glashow model
A spherically symmetric excitations of the Polyakov - t' Hooft monopole are considered. In the framework of the geodesics deviation equation it is found that in the large mass Higgs sector a…
Tomasz Dobrowolski, Jerzy SzczesnyJan 12, 1999
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Geodesics deviation equation approach to chaos
Geodesics deviation equation (GDE) is itroduced. In "adiabatic" approximation exact solution of the GDE if found. Perturbation theory in general case is formulated. Geometrical criterion of…
Tomasz Dobrowolski, Jerzy SzczesnyJan 12, 1999
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Asymptotic Theory for the Probability Density Functions in Burgers Turbulence
A rigorous study is carried out for the randomly forced Burgers equation in the inviscid limit. No closure approximations are made. Instead the probability density functions of velocity and velocity…
Weinan E, Eric Vanden EijndenJan 8, 1999
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The Lorenz model as a singularly perturbed nonlinear system
A method of expansion of solutions of singularly perturbed nonlinear systems in power series of small parameters is applied to the popular Lorenz model in synergetics.Simple asymptotic expressions…
E. M. ShahverdievJan 8, 1999
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Exponentially small oscillation of 2-dimensional stable and unstable manifolds in 4-dimensional symplectic mappings
Homoclinic bifurcation of 4-dimensional symplectic mappings is asymptotically studied. We construct the 2-dimensional stable and unstable manifolds near the sub-manifolds which experience…
Yoshihiro Hirata, Kazuhiro Nozaki, Tetsuro KonishiJan 6, 1999
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Bicritical Behavior of Period Doublings in Unidirectionally-Coupled Maps
We study the scaling behavior of period doublings in two unidirectionally-coupled one-dimensional maps near a bicritical point where two critical lines of period-doubling transition to chaos in both…
Sang-Yoon KimJan 6, 1999
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Quantum Lévy Processes and Fractional Kinetics
Exotic stochastic processes are shown to emerge in the quantum evolution of complex systems. Using influence function techniques, we consider the dynamics of a system coupled to a chaotic subsystem…
Dimitri Kusnezov, Aurel Bulgac, Giu Do DangJan 4, 1999
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Periodic orbit sum rules for billiards: Accelerating cycle expansions
We show that the periodic orbit sums for 2-dimensional billiards satisfy an infinity of exact sum rules. We test such sum rules and demonstrate that they can be used to accelerate the convergence of…
Sune F. Nielsen, Per Dahlqvist, Predrag CvitanovicJan 4, 1999
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Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics
This paper reviews various applications of the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mechanics. We adopt a new point of view which has emerged…
David RuelleDec 31, 1998
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Fractals of the Julia and Mandelbrot sets of the Riemann Zeta Function
Computations of the Julia and Mandelbrot sets of the Riemann zeta function and observations of their properties are made. In the appendix section, a corollary of Voronin's theorem is derived and…
S. C. WoonDec 27, 1998
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Testing for General Dynamical Stationarity with a Symbolic Data Compression Technique
We construct a statistic and null test for examining the stationarity of time-series of discrete symbols: whether two data streams appear to originate from the same underlying unknown dynamical…
Matthew B. Kennel, Alistair I. MeesDec 23, 1998
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Numerical Analysis of Dynamical Systems and the Fractal Dimension of Boundaries
A set of MapleV R.4/5 software routines for calculating the numerical evolution of dynamical systems and flexibly plotting the results is presented. The package consists of an initial condition…
L. G. S. Duarte, L. A. C. P. da Mota, H. P. de Oliveira et al.Dec 22, 1998
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Amplitude Equations for Reaction-Diffusion Systems with a Hopf Bifurcation and Slow Real Modes
Using a normal form approach described in a previous paper we derive an amplitude equation for a reaction-diffusion system with a Hopf bifurcation coupled to one or more slow real eigenmodes. The new…
M. Ipsen, F. Hynne, P. G. SoerensenDec 21, 1998
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Chaotic Autoionization of the Relativistic Two-Electron Atom
Chaotic autoionization of the relativistic two-electron atom is investigated. A theoretical analysis of chaotic dynamics of the relativistic outer electron under the periodic perturbation due to the…
D. U. MatrasulovDec 21, 1998
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Conformal Theory of the Dimensions of Diffusion Limited Aggregates
We employ the recently introduced conformal iterative construction of Diffusion Limited Aggregates (DLA) to study the multifractal properties of the harmonic measure. The support of the harmonic…
Benny Davidovich, Itamar ProcacciaDec 20, 1998
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Fractal dimension of space-time chaos
A class of simplified measures is constructed to capture the key features of generic spatio-temporally chaotic systems. A combined analytical and numerical investigation allows us to extablish the…
Antonio Politi, Annette WittDec 17, 1998
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The dynamics of a low-order coupled ocean-atmosphere model
A system of five ordinary differential equations is studied which combines the Lorenz-84 model for the atmosphere and a box model for the ocean. The behaviour of this system is studied as a function…
L. van Veen, F. Verhulst, T. OpsteeghDec 16, 1998
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