Biological Physics Section, Max Planck Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, Dresden 01187, Germany.
Philos Trans A Math Phys Eng Sci. 2013 Aug 19;371(1999):20120462. doi: 10.1098/rsta.2012.0462. Print 2013 Sep 28.
Amplitude death is a dynamical phenomenon in which a network of oscillators settles to a stable state as a result of coupling. Here, we study amplitude death in a generalized model of delay-coupled delay oscillators. We derive analytical results for degree homogeneous networks which show that amplitude death is governed by certain eigenvalues of the network's adjacency matrix. In particular, these results demonstrate that in delay-coupled delay oscillators amplitude death can occur for arbitrarily large coupling strength k. In this limit, we find a region of amplitude death which already occurs at small coupling delays that scale with 1/k. We show numerically that these results remain valid in random networks with heterogeneous degree distribution.
幅度死亡是一种动力学现象，其中振荡器网络由于耦合而稳定到稳定状态。在这里，我们研究了具有延迟耦合延迟振荡器的广义模型中的幅度死亡。我们为度均匀网络推导出了解析结果，这些结果表明幅度死亡由网络邻接矩阵的某些特征值控制。特别是，这些结果表明在延迟耦合延迟振荡器中，幅度死亡可以在任意大的耦合强度 k 下发生。在这个极限下，我们发现幅度死亡区域已经出现在与 1/k 成比例的小耦合延迟中。我们数值表明，这些结果在具有异质度分布的随机网络中仍然有效。
