arXiv 0802.30242008-02-21nlin.CD

空间扩展系统非平衡相变的混沌同步

Chaotic synchronizations of spatially extended systems as non-equilibrium phase transitions

M. Cencini, C. J. Tessone, A. Torcini

备注：: 12 pages, 5 figures Comments are welcome
发表信息：: Chaos 18, 037125 (2008)
DOI：: 10.1063/1.2945903

摘要：

两个空间扩展混沌系统的副本同步到一个共同的时空混沌状态时，耦合超过一个临界强度。作为一个原型的每个单一的时空混沌系统的映射格通过幂律耦合相互作用被认为是。将同步转变作为一种非平衡相变来研究，分析了在不同的空间相互作用范围以及组成每个系统的动力学单元的非线性下，同步转变的临界性质。特别是，连续和不连续的局部映射被认为是。在这两种情况下的过渡是二阶的临界指数随指数表征的相互作用范围。对于不连续的地图，它的数值表明，过渡属于{ \it异常定向渗流}（ADP）家庭的普遍性类，以前确定的L{é} vy飞行传播的流行病过程。对于连续映射，临界指数是不同的特征ADP，但除了最近邻的情况下，相应的普适类的识别仍然是一个悬而未决的问题。最后，为了检验确定性相关对所研究的同步跃迁的影响，用合适的随机模型代替混沌动力学演化。在这个框架和不连续的情况下，它是可能的，以获得一个有效的朗之万描述，对应于ADP的建议。

英文摘要：

Two replicas of spatially extended chaotic systems synchronize to a common spatio-temporal chaotic state when coupled above a critical strength. As a prototype of each single spatio-temporal chaotic system a lattice of maps interacting via power-law coupling is considered. The synchronization transition is studied as a non-equilibrium phase transition, and its critical properties are analyzed at varying the spatial interaction range as well as the nonlinearity of the dynamical units composing each system. In particular, continuous and discontinuous local maps are considered. In both cases the transitions are of the second order with critical indexes varying with the exponent characterizing the interaction range. For discontinuous maps it is numerically shown that the transition belongs to the {\it anomalous directed percolation} (ADP) family of universality classes, previously identified for L{é}vy-flight spreading of epidemic processes. For continuous maps, the critical exponents are different from those characterizing ADP, but apart from the nearest-neighbor case, the identification of the corresponding universality classes remains an open problem. Finally, to test the influence of deterministic correlations for the studied synchronization transitions, the chaotic dynamical evolutions are substituted by suitable stochastic models. In this framework and for the discontinuous case, it is possible to derive an effective Langevin description that corresponds to that proposed for ADP.

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摘要：

英文摘要：

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