Centre for Systems, Dynamics and Control, Department of Mathematics, University of Exeter, Exeter EX4 4QF, United Kingdom.
Chaos. 2021 Sep;31(9):093132. doi: 10.1063/5.0063423.
A dead zone in the interaction between two dynamical systems is a region of their joint phase space where one system is insensitive to the changes in the other. These can arise in a number of contexts, and their presence in phase interaction functions has interesting dynamical consequences for the emergent dynamics. In this paper, we consider dead zones in the interaction of general coupled dynamical systems. For weakly coupled limit cycle oscillators, we investigate criteria that give rise to dead zones in the phase interaction functions. We give applications to coupled multiscale oscillators where coupling on only one branch of a relaxation oscillation can lead to the appearance of dead zones in a phase description of their interaction.
两个动力系统之间相互作用的死区是它们的联合相空间中的一个区域，在这个区域中，一个系统对另一个系统的变化不敏感。这些死区可能出现在许多情况下，它们在相位相互作用函数中的存在对涌现动力学具有有趣的动力学后果。在本文中，我们考虑了一般耦合动力系统相互作用中的死区。对于弱耦合的极限环振荡器，我们研究了导致相位相互作用函数中出现死区的准则。我们将其应用于耦合多尺度振荡器中，其中仅在弛豫振荡的一个分支上的耦合就可以导致它们相互作用的相位描述中出现死区。
