Analysis of chaotic motion and its shape dependence in a generalized piecewise linear map

We analyse the chaotic motion and its shape dependence in a piecewise linear map using Fujisaka's characteristic function method. The map is a generalization of the one introduced by R. Artuso. Exact expressions for diffusion coefficient are obtained giving previously obtained results as special cases. Fluctuation spectrum relating to probability density function is obtained in a parametric form. We also give limiting forms of the above quantities. Dependence of diffusion coefficient and probability density function on the shape of the map is examined.Comment: 4 pages,4 figure

Mapping Model of Chaotic Phase Synchronization

A coupled map model for the chaotic phase synchronization and its desynchronization phenomenon is proposed. The model is constructed by integrating the coupled kicked oscillator system, kicking strength depending on the complex state variables. It is shown that the proposed model clearly exhibits the chaotic phase synchronization phenomenon. Furthermore, we numerically prove that in the region where the phase synchronization is weakly broken, the anomalous scaling of the phase difference rotation number is observed. This proves that the present model belongs to the same universality class found by Pikovsky et al.. Furthermore, the phase diffusion coefficient in the de-synchronization state is analyzed.Comment: Accepted for publication in Prog. Theor. Phy

Coarse-graining and Self-similarity of Price Fluctuations

We propose a new approach for analyzing price fluctuations in their strongly correlated regime ranging from minutes to months. This is done by employing a self-similarity assumption for the magnitude of coarse-grained price fluctuation or volatility. The existence of a Cramer function, the characteristic function for self-similarity, is confirmed by analyzing real price data from a stock market. We also discuss the close interrelation among our approach, the scaling-of-moments method and the multifractal approach for price fluctuations.Comment: 9 pages, 3 figure

Continued-fraction expansion of eigenvalues of generalized evolution operators in terms of periodic orbits

A new expansion scheme to evaluate the eigenvalues of the generalized evolution operator (Frobenius-Perron operator) $H_{q}$ relevant to the fluctuation spectrum and poles of the order-$q$ power spectrum is proposed. The ``partition function'' is computed in terms of unstable periodic orbits and then used in a finite pole approximation of the continued fraction expansion for the evolution operator. A solvable example is presented and the approximate and exact results are compared; good agreement is found.Comment: CYCLER Paper 93mar00

Synchronization of Coupled Systems with Spatiotemporal Chaos

We argue that the synchronization transition of stochastically coupled cellular automata, discovered recently by L.G. Morelli {\it et al.} (Phys. Rev. {\bf 58 E}, R8 (1998)), is generically in the directed percolation universality class. In particular, this holds numerically for the specific example studied by these authors, in contrast to their claim. For real-valued systems with spatiotemporal chaos such as coupled map lattices, we claim that the synchronization transition is generically in the universality class of the Kardar-Parisi-Zhang equation with a nonlinear growth limiting term.Comment: 4 pages, including 3 figures; submitted to Phys. Rev.

TURING INSTABILITY IN THE OREGONATOR MODEL(Session IV : Structures & Patterns, The 1st Tohwa University International Meeting on Statistical Physics Theories, Experiments and Computer Simulations)

この論文は国立情報学研究所の電子図書館事業により電子化されました

Phase synchronization in time-delay systems

Though the notion of phase synchronization has been well studied in chaotic dynamical systems without delay, it has not been realized yet in chaotic time-delay systems exhibiting non-phase coherent hyperchaotic attractors. In this article we report the first identification of phase synchronization in coupled time-delay systems exhibiting hyperchaotic attractor. We show that there is a transition from non-synchronized behavior to phase and then to generalized synchronization as a function of coupling strength. These transitions are characterized by recurrence quantification analysis, by phase differences based on a new transformation of the attractors and also by the changes in the Lyapunov exponents. We have found these transitions in coupled piece-wise linear and in Mackey-Glass time-delay systems.Comment: 4 pages, 3 Figures (To appear in Physical Review E Rapid Communication

From synchronization to Lyapunov exponents and back

The goal of this paper is twofold. In the first part we discuss a general approach to determine Lyapunov exponents from ensemble- rather than time-averages. The approach passes through the identification of locally stable and unstable manifolds (the Lyapunov vectors), thereby revealing an analogy with generalized synchronization. The method is then applied to a periodically forced chaotic oscillator to show that the modulus of the Lyapunov exponent associated to the phase dynamics increases quadratically with the coupling strength and it is therefore different from zero already below the onset of phase-synchronization. The analytical calculations are carried out for a model, the generalized special flow, that we construct as a simplified version of the periodically forced Rossler oscillator.Comment: Submitted to Physica