Topic
Coupled map lattice
About: Coupled map lattice is a research topic. Over the lifetime, 1390 publications have been published within this topic receiving 28075 citations.
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01 Jan 2003
TL;DR: In this article, the basic principles of direct chaotic communications are presented for modeling diversity by chaos and classification by synchronization in high-dimensional dynamical systems, including cycled attractors of coupled cell systems and dynamics with symmetry.
Abstract: Cycling attractors of coupled cell systems and dynamics with symmetry- Modelling diversity by chaos and classification by synchronization- Basic Principles of Direct Chaotic Communications- Prevalence of Milnor Attractors and Chaotic Itinerancy in 'High'-dimensional Dynamical Systems- Generalization of the Feigenbaum-Kadanoff-Shenker Renormalization and Critical Phenomena Associated with the Golden Mean Quasiperiodicity- Synchronization and clustering in ensembles of coupled chaotic oscillators- Nonlinear Phenomena in Nephron-Nephron Interaction- Synchrony in Globally Coupled Chaotic, Periodic, and Mixed Ensembles of Dynamical Units- Phase synchronization of regular and chaotic self-sustained oscillators- Control of dynamical systems via time-delayed feedback and unstable controller
1,081 citations
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TL;DR: The horizontal visibility algorithm as mentioned in this paper is a geometrically simpler and analytically solvable version of our former algorithm, focusing on the mapping of random series series of independent identically distributed random variables.
Abstract: networks. This procedure allows us to apply methods of complex network theory for characterizing time series. In this work we present the horizontal visibility algorithm, a geometrically simpler and analytically solvable version of our former algorithm, focusing on the mapping of random series series of independent identically distributed random variables. After presenting some properties of the algorithm, we present exact results on the topological properties of graphs associated with random series, namely, the degree distribution, the clustering coefficient, and the mean path length. We show that the horizontal visibility algorithm stands as a simple method to discriminate randomness in time series since any random series maps to a graph with an exponential degree distribution of the shape Pk=1 /32 /3 k2 , independent of the probability distribution from which the series was generated. Accordingly, visibility graphs with other Pk are related to nonrandom series. Numerical simulations confirm the accuracy of the theorems for finite series. In a second part, we show that the method is able to distinguish chaotic series from independent and identically distributed i.i.d. theory, studying the following situations: i noise-free low-dimensional chaotic series, ii low-dimensional noisy chaotic series, even in the presence of large amounts of noise, and iii high-dimensional chaotic series coupled map lattice, without needs for additional techniques such as surrogate data or noise reduction methods. Finally, heuristic arguments are given to explain the topological properties of chaotic series, and several sequences that are conjectured to be random are analyzed.
547 citations
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TL;DR: It was demonstrated that one can convert the motion of a chaotic dynamical system to periodic motion by controlling the system about one of the many unstable periodic orbits embedded in the chaotic attractor, through only small time dependent perturbations in an accessible system parameter.
Abstract: It was demonstrated that one can convert the motion of a chaotic dynamical system to periodic motion by controlling the system about one of the many unstable periodic orbits embedded in the chaotic attractor, through only small time dependent perturbations in an accessible system parameter. They demonstrated their method numerically by controlling the Henon map. Far from being a numerical curiosity that requires experimentally unattainable precision, it was believed that this method can be widely implemented in a variety of systems including chemical, biological, optical, electronic, and mechanical systems. The method is based on the observation that unstable periodic orbits are dense in a typical chaotic attractor. Their method assumes only the following four points. First, the dynamics of the system can be represented as arising from an n-dimensional non-linear map. Second, there is a specific periodic orbit of the map which lies in the attractor and around which one wishes to stabilize the dynamics, and so on. To control the chaos, one attempts to confine the iterates of the map to a small neighborhood of the desired orbit.
545 citations