Synchronisation and scaling properties of chaotic networks with multiple delays
Synchronisation and scaling properties of chaotic networks with multiple delays
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DOI：
10.1209/0295-5075/103/10013
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发表时间：
2013-07-01
期刊：
影响因子：
1.8
通讯作者：
Kinzel, Wolfgang
中科院分区：
文献类型：
--
作者：
D'Huys, Otti;Zeeb, Steffen;Kinzel, Wolfgang
我们研究具有多个数量级的多个时间延迟的混沌系统。我们表明，此类系统中的李亚普诺夫指数（LE）谱具有分层结构，不同部分随不同延迟而缩放。这会导致不同类型的混乱，具体取决于最大 LE 的缩放比例。我们的结果特别与分层网络（网络的网络）的同步特性相关，其中子网络的节点以较短的延迟耦合，不同子网络之间的耦合以较长的延迟时间实现。如果最大指数以较短的延迟缩放，则子网内的单元可以同步，只有当最大指数以较长的延迟缩放时，不同子网之间的远程同步才可能。结果对伯努利图进行了分析说明，对帐篷图和半导体激光器进行了数值说明。版权所有 (c) EPLA，2013
We study chaotic systems with multiple time delays that range over several orders of magnitude. We show that the spectrum of Lyapunov exponents (LEs) in such systems possesses a hierarchical structure, with different parts scaling with the different delays. This leads to different types of chaos, depending on the scaling of the maximal LE. Our results are relevant, in particular, for the synchronisation properties of hierarchical networks (networks of networks) where the nodes of subnetworks are coupled with shorter delays and couplings between different subnetworks are realised with longer delay times. Units within a subnetwork can synchronise if the maximal exponent scales with the shorter delay, long-range synchronisation between different subnetworks is only possible if the maximal exponent scales with the longer delay. The results are illustrated analytically for Bernoulli maps and numerically for tent maps and semiconductor lasers. Copyright (c) EPLA, 2013