论文标题
在耦合的逻辑图中过渡到粗粒顺序：延迟和不对称的影响
Transition to Coarse-Grained Order in Coupled Logistic Maps: Effect of Delay and Asymmetry
论文作者
论文摘要
我们研究了一维耦合的逻辑图，并使用延迟的线性或非线性邻邻耦合。以映射x*为参考的非零固定点，我们通过以旋转状态和低于x*的值识别x*上方的值来粗糙晶粒。我们将时间t定义为持续的位点，因为该位点甚至在时间t之前都不会改变其旋转状态。过渡伴随着抗铁磁或铁磁在太空中的出现。我们观察到非线性耦合甚至延迟，或线性耦合和奇数延迟的抗铁磁顺序。我们观察到线性耦合甚至延迟，非线性耦合和奇数延迟的铁磁顺序。对于对称耦合，我们观察到持久性的幂律衰减。持久性指数接近0.375，用于过渡到抗磁磁序，而对于铁磁序的持续时间接近0.285。在所有情况下，域壁的数量在所有情况下衰减，指数接近0.5。在存在不对称的情况下，持久性是在临界点的拉伸指数而不是幂律。
We study one-dimensional coupled logistic maps with delayed linear or nonlinear nearest-neighbor coupling. Taking the nonzero fixed point of the map x* as reference, we coarse-grain the system by identifying values above x* with the spin-up state and values below x* with the spin-down state. We define persistent sites at time T as the sites which did not change their spin state even once for all even times till time T. A clear transition from asymptotic zero persistence to non-zero persistence is seen in the parameter space. The transition is accompanied by the emergence of antiferromagnetic, or ferromagnetic order in space. We observe antiferromagnetic order for nonlinear coupling and even delay, or linear coupling and odd delay. We observe ferromagnetic order for linear coupling and even delay, or nonlinear coupling and odd delay. For symmetric coupling, we observe a power-law decay of persistence. The persistence exponent is close to 0.375 for the transition to antiferromagnetic order and close to 0.285 for ferromagnetic order. The number of domain walls decays with an exponent close to 0.5 in all cases as expected. The persistence decays as a stretched exponential and not a power-law at the critical point, in the presence of asymmetry.
