Hart Joseph D, Larger Laurent, Murphy Thomas E, Roy Rajarshi
Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD 20742, USA.
Department of Physics, University of Maryland, College Park, MD 20742, USA.
Philos Trans A Math Phys Eng Sci. 2019 Sep 9;377(2153):20180123. doi: 10.1098/rsta.2018.0123. Epub 2019 Jul 22.
We present a systematic approach to reveal the correspondence between time delay dynamics and networks of coupled oscillators. After early demonstrations of the usefulness of spatio-temporal representations of time-delay system dynamics, extensive research on optoelectronic feedback loops has revealed their immense potential for realizing complex system dynamics such as chimeras in rings of coupled oscillators and applications to reservoir computing. Delayed dynamical systems have been enriched in recent years through the application of digital signal processing techniques. Very recently, we have showed that one can significantly extend the capabilities and implement networks with arbitrary topologies through the use of field programmable gate arrays. This architecture allows the design of appropriate filters and multiple time delays, and greatly extends the possibilities for exploring synchronization patterns in arbitrary network topologies. This has enabled us to explore complex dynamics on networks with nodes that can be perfectly identical, introduce parameter heterogeneities and multiple time delays, as well as change network topologies to control the formation and evolution of patterns of synchrony. This article is part of the theme issue 'Nonlinear dynamics of delay systems'.
我们提出了一种系统方法来揭示时间延迟动力学与耦合振子网络之间的对应关系。在早期证明了时间延迟系统动力学的时空表示的有用性之后，对光电反馈回路的广泛研究揭示了它们在实现复杂系统动力学方面的巨大潜力，例如耦合振子环中的奇异态以及在储层计算中的应用。近年来，通过数字信号处理技术的应用，延迟动力系统得到了丰富。最近，我们表明通过使用现场可编程门阵列，可以显著扩展能力并实现具有任意拓扑结构的网络。这种架构允许设计合适的滤波器和多个时间延迟，并极大地扩展了在任意网络拓扑中探索同步模式的可能性。这使我们能够在具有完全相同节点的网络上探索复杂动力学，引入参数异质性和多个时间延迟，以及改变网络拓扑以控制同步模式的形成和演化。本文是主题为“延迟系统的非线性动力学”的一部分。
