Droz Michel, Lipowski Adam
Department of Physics, University of Geneva, CH 1211 Geneva 4, Switzerland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 May;67(5 Pt 2):056204. doi: 10.1103/PhysRevE.67.056204. Epub 2003 May 13.
We use spreading dynamics to study the synchronization transition (ST) of one-dimensional coupled map lattices (CML's). Recently, Baroni et al. [Phys. Rev. E 63, 036226 (2001)] have shown that the ST belongs to the directed percolation (DP) universality class for discontinuous CML's. This was confirmed by accurate numerical simulations for the Bernoulli map by Ahlers and Pikovsky [Phys. Rev. Lett. 88, 254101 (2002)]. Spreading dynamics confirms such an identification only for random synchronized states. For homogeneous synchronized states the spreading exponents eta and delta are different from the DP exponents but their sum equals the corresponding sum of the DP exponents. Such a relation is typical of models with infinitely many absorbing states. Moreover, we calculate the spreading exponents for the tent map for which the ST belongs to the bounded Kardar-Parisi-Zhang (BKPZ) universality class. The estimation of spreading exponents for random synchronized states is consistent with the hyperscaling relation, while it is inconsistent for the homogeneous ones. Finally, we examine the asymmetric tent map. For small asymmetry the ST remains of the BKPZ type. However, for large asymmetry a different critical behavior appears, with exponents being relatively close to those for DP.
我们使用传播动力学来研究一维耦合映射格点（CML）的同步转变（ST）。最近，巴罗尼等人[《物理评论E》63，036226（2001）]表明，对于不连续的CML，ST属于定向渗流（DP）普适类。阿勒斯和皮科夫斯基[《物理评论快报》88，254101（2002）]对伯努利映射进行的精确数值模拟证实了这一点。传播动力学仅对随机同步态证实了这种识别。对于均匀同步态，传播指数η和δ与DP指数不同，但它们的和等于DP指数的相应和。这种关系是具有无限多个吸收态的模型所特有的。此外，我们计算了ST属于有界卡达尔 - 帕里西 - 张（BKPZ）普适类的帐篷映射的传播指数。对随机同步态的传播指数估计与超标度关系一致，而对均匀同步态则不一致。最后，我们研究了非对称帐篷映射。对于小的不对称性，ST仍然属于BKPZ类型。然而，对于大的不对称性，会出现不同的临界行为，其指数相对接近DP的指数。
