Phase transitions in a piecewise expanding coupled map lattice with linear nearest neighbour coupling
Phase transitions in a piecewise expanding coupled map lattice with linear nearest neighbour coupling
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DOI：
10.1088/0951-7715/19/9/012
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发表时间：
2006-05
期刊：
影响因子：
1.7
通讯作者：
Jean-Baptiste Bardet;G. Keller
中科院分区：
文献类型：
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作者：
Jean-Baptiste Bardet;G. Keller
我们在 [−1, 1] 上构造一个混合连续分段线性映射，其特性是由这些映射组成的二维晶格具有线性北和东最近邻耦合，允许相变。我们还提供了这种结构的修改，其中局部地图是扩展的解析圆地图。基本策略借鉴自 Gielis 和 MacKay (2000 Nonlinearity 13 867–88)；也就是说，我们将 CML 的动力学与 Toom 类型的概率元胞自动机的动力学进行比较；有关详细讨论，请参阅 MacKay (2005 Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems (Lecture Notes in Chemistry vol 671) ed J-R Chazottes and B Fernandez (Berlin: Springer) pp 65-94）。
We construct a mixing continuous piecewise linear map on [−1, 1] with the property that a two-dimensional lattice made of these maps with a linear north and east nearest neighbour coupling admits a phase transition. We also provide a modification of this construction where the local map is an expanding analytic circle map. The basic strategy is borrowed from Gielis and MacKay (2000 Nonlinearity 13 867–88); namely, we compare the dynamics of the CML with those of a probabilistic cellular automaton of Toom's type; see MacKay (2005 Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems (Lecture Notes in Physics vol 671) ed J-R Chazottes and B Fernandez (Berlin: Springer) pp 65–94) for a detailed discussion.