具有双稳态热力学极限的随机稳定全局耦合映射
Stochastically stable globally coupled maps with bistable thermodynamic limit
摘要：
我们研究系统的全球耦合区间映射，其中相同的个人地图有两个扩展，分数线性，到分支，并通过一个参数引入耦合-共同的所有个人地图-这取决于在一个分析的方式上的平均场的系统。我们展示：1）在我们所考虑的耦合参数范围内，有限大小耦合系统总是有唯一的严格正的解析不变概率密度，并且所有的有限大小耦合系统的相关性都是指数衰减的。2)对于相同的参数范围内，自洽Perron-Frobenius算子，捕获相应的无限大系统的基本方面（出现上述的限制时，系统的大小趋于无穷大），经历了一个超临界的干草叉分叉从一个唯一的稳定平衡共存的两个稳定和一个不稳定的平衡。
英文摘要：
We study systems of globally coupled interval maps, where the identical individual maps have two expanding, fractional linear, onto branches, and where the coupling is introduced via a parameter - common to all individual maps - that depends in an analytic way on the mean field of the system. We show: 1) For the range of coupling parameters we consider, finite-size coupled systems always have a unique invariant probability density which is strictly positive and analytic, and all finite-size systems exhibit exponential decay of correlations. 2) For the same range of parameters, the self-consistent Perron-Frobenius operator which captures essential aspects of the corresponding infinite-size system (arising as the limit of the above when the system size tends to infinity), undergoes a supercritical pitchfork bifurcation from a unique stable equilibrium to the coexistence of two stable and one unstable equilibrium.
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