延迟动力系统：网络、嵌合体与储备池计算
Delayed Dynamical Systems: Networks, Chimeras and Reservoir Computing
AI总结：
本文提出利用FPGA和数字信号处理构建任意拓扑延迟网络，以研究耦合振子网络中的嵌合体、同步模式及储备池计算应用。
摘要：
我们提出一种系统性方法，以揭示时间延迟动力学与耦合振子网络之间的对应关系。在早期证明时间延迟系统动力学的时空表示具有实用性之后，关于光电反馈环的大量研究已揭示其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嵌合体（chimeras）以及在储备池计算（reservoir computing）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进一步丰富。最近，我们证明了可以通过使用现场可编程门阵列（FPGAs）显著扩展其能力，并实现具有任意拓扑结构的网络。该架构允许设计适当的滤波器和多重时间延迟，从而极大地拓展了在任意拓扑网络中探索同步模式的可能性。这使我们能够在节点可以完全相同的网络上探索复杂动力学，引入参数异质性和多重时间延迟，并改变网络拓扑以控制同步模式的形成与演化。
英文摘要：
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 (FPGAs). This architecture allows the design of appropriate filters and multiple time delays which greatly extend the possibilities for exploring synchronization patterns in arbitrary topological networks. 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.
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