Banerjee Tanmoy, Paul Bishwajit, Sarkar B C
Department of Physics, University of Burdwan, Burdwan, West Bengal 713 104, India.
Chaos. 2014 Mar;24(1):013116. doi: 10.1063/1.4863859.
We explore the spatiotemporal dynamics of a coupled map lattice (CML) system, which is realized with a one dimensional array of locally coupled digital phase-locked loops (DPLLs). DPLL is a nonlinear feedback-controlled system widely used as an important building block of electronic communication systems. We derive the phase-error equation of the spatially extended system of coupled DPLLs, which resembles a form of the equation of a CML system. We carry out stability analysis for the synchronized homogeneous solutions using the circulant matrix formalism. It is shown through extensive numerical simulations that with the variation of nonlinearity parameter and coupling strength the system shows transitions among several generic features of spatiotemporal dynamics, viz., synchronized fixed point solution, frozen random pattern, pattern selection, spatiotemporal intermittency, and fully developed spatiotemporal chaos. We quantify the spatiotemporal dynamics using quantitative measures like average quadratic deviation and spatial correlation function. We emphasize that instead of using an idealized model of CML, which is usually employed to observe the spatiotemporal behaviors, we consider a real world physical system and establish the existence of spatiotemporal chaos and other patterns in this system. We also discuss the importance of the present study in engineering application like removal of clock-skew in parallel processors.
我们研究了耦合映射格点（CML）系统的时空动力学，该系统由一维局部耦合数字锁相环（DPLL）阵列实现。DPLL是一种非线性反馈控制系统，广泛用作电子通信系统的重要组成部分。我们推导了耦合DPLL空间扩展系统的相位误差方程，该方程类似于CML系统方程的形式。我们使用循环矩阵形式对同步均匀解进行稳定性分析。通过大量数值模拟表明，随着非线性参数和耦合强度的变化，系统呈现出时空动力学的几种一般特征之间的转变，即同步不动点解、冻结随机模式、模式选择、时空间歇性和完全发展的时空混沌。我们使用平均二次偏差和空间相关函数等定量指标来量化时空动力学。我们强调，我们考虑的是一个现实世界的物理系统，而不是通常用于观察时空行为的理想化CML模型，并在该系统中建立了时空混沌和其他模式的存在性。我们还讨论了本研究在工程应用中的重要性，如消除并行处理器中的时钟偏差。
