Janaki T M, Sinha Sudeshna, Gupte Neelima
Institute of Mathematical Sciences, Taramani, Chennai 600 113, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 May;67(5 Pt 2):056218. doi: 10.1103/PhysRevE.67.056218. Epub 2003 May 27.
We consider a lattice of coupled circle maps, a popular model for the study of mode-locked phenomena. We find that the onset of spatiotemporal intermittency (STI) in this system is analogous to directed percolation (DP), with the transition being to a unique absorbing state for low nonlinearities, and to weakly chaotic absorbing states for high nonlinearities. We find that the complete set of static exponents and spreading exponents at all critical points match those of DP very convincingly. Further, hyperscaling relations are fulfilled, leading to independent controls and consistency checks of the values of all the critical exponents. These results provide an example in support of the conjecture that the onset of STI in deterministic models belongs to the DP universality class. Nonuniversal spreading exponents are seen only for the cases where the initial state is homogeneous with symmetrically placed seeds leading to strictly symmetric spreading. However, very small departures from homogeneity are sufficient to restore the DP exponents.
我们考虑一个耦合圆映射晶格，这是研究锁模现象的一个常用模型。我们发现，该系统中时空间歇性（STI）的起始类似于定向渗流（DP），对于低非线性，转变为一个唯一的吸收态，而对于高非线性，则转变为弱混沌吸收态。我们发现，所有临界点处的静态指数和传播指数的完整集合与DP的指数非常令人信服地匹配。此外，超标度关系成立，从而对所有临界指数的值进行独立控制和一致性检验。这些结果提供了一个例子，支持了确定性模型中STI的起始属于DP普适类的猜想。仅在初始状态是均匀的且具有对称放置的种子从而导致严格对称传播的情况下，才会出现非普适传播指数。然而，与均匀性的非常小的偏差就足以恢复DP指数。
