Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA, 92093, USA.
Department of Information Engineering, University of Padova, Padova, 35131, Italy.
Nat Commun. 2022 Aug 11;13(1):4721. doi: 10.1038/s41467-022-31733-2.
Oscillatory activity is ubiquitous in natural and engineered network systems. The interaction scheme underlying interdependent oscillatory components governs the emergence of network-wide patterns of synchrony that regulate and enable complex functions. Yet, understanding, and ultimately harnessing, the structure-function relationship in oscillator networks remains an outstanding challenge of modern science. Here, we address this challenge by presenting a principled method to prescribe exact and robust functional configurations from local network interactions through optimal tuning of the oscillators' parameters. To quantify the behavioral synchrony between coupled oscillators, we introduce the notion of functional pattern, which encodes the pairwise relationships between the oscillators' phases. Our procedure is computationally efficient and provably correct, accounts for constrained interaction types, and allows to concurrently assign multiple desired functional patterns. Further, we derive algebraic and graph-theoretic conditions to guarantee the feasibility and stability of target functional patterns. These conditions provide an interpretable mapping between the structural constraints and their functional implications in oscillator networks. As a proof of concept, we apply the proposed method to replicate empirically recorded functional relationships from cortical oscillations in a human brain, and to redistribute the active power flow in different models of electrical grids.
振荡活动在自然和工程网络系统中无处不在。相依振荡元件的相互作用方案控制着网络范围内同步模式的出现，这些模式调节和支持复杂功能。然而，理解和最终利用振荡器网络的结构-功能关系仍然是现代科学的一个突出挑战。在这里，我们通过最优调整振荡器的参数，从局部网络相互作用中规定精确和稳健的功能配置，来解决这一挑战。为了量化耦合振荡器之间的行为同步，我们引入了功能模式的概念，它编码了振荡器相位之间的两两关系。我们的方法计算效率高，证明是正确的，考虑到了约束的相互作用类型，并允许同时分配多个期望的功能模式。此外，我们推导出了代数和图论条件，以保证目标功能模式的可行性和稳定性。这些条件提供了振荡器网络中结构约束与其功能影响之间的可解释映射。作为一个概念验证，我们将所提出的方法应用于复制人类大脑皮质振荡中经验记录的功能关系，并重新分配不同电力网格模型中的有效功率流。
