Roy Anupama, Gupte Neelima
Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India.
Chaos. 2022 Jan;32(1):013120. doi: 10.1063/5.0055291.
We study the transition to synchronization on hierarchical lattices using the evolution of Chaté-Manneville maps placed on a triangular lattice. Connections are generated between the levels of the triangular lattice, assuming that each site is connected to its neighbors on the level below with probability half. The maps are diffusively coupled, and the map parameters increase hierarchically, depending on the map parameters at the sites they are coupled to in the previous level. The system shows a transition to synchronization, which is second order in nature, with associated critical exponents. However, the V-lattice, which is a special realization of this lattice, shows a transition to synchronization that is discontinuous with accompanying hysteretic behavior. This transition can thus be said to belong to the class of explosive synchronization with the explosive nature depending on the nature of the substrate. We carry out finite-size-finite-time scaling for the continuous transition and analyze the scaling of the jump size for the discontinuous case. We discuss the implications of our results and draw parallels with avalanche statistics on branching hierarchical lattices.
我们利用置于三角格点上的Chaté-Manneville映射的演化来研究层次格点上的同步转变。在三角格点的各层之间建立连接，假设每个格点以概率二分之一与其下方层的相邻格点相连。这些映射通过扩散耦合，并且映射参数根据它们在前一层中耦合的格点处的映射参数分层增加。该系统显示出向同步的转变，这本质上是二阶的，具有相关的临界指数。然而，V型格点作为这种格点的一种特殊实现，显示出向同步的不连续转变，并伴有滞后行为。因此，这种转变可以说是属于爆炸同步类别，其爆炸性质取决于底物的性质。我们对连续转变进行有限尺寸 - 有限时间标度，并分析不连续情况下跳跃大小的标度。我们讨论了我们结果的含义，并与分支层次格点上的雪崩统计进行了比较。
