We investigate the existence of an optimal interplay between the naturalfrequencies of a group chaotic oscillators and the topological properties ofthe network they are embedded in. We identify the conditions for achievingphase synchronization in the most effective way, i.e., with the lowest possiblecoupling strength. Specifically, we show by means of numerical and experimentalresults that it is possible to define a synchrony alignment function linkingthe natural frequencies of a set of non-identical phase-coherent chaoticoscillators with the topology of the Laplacian matrix $L$, the latteraccounting for the specific organization of the network of interactions betweenoscillators. We use the classical R\"ossler system to show that the synchronyalignment function obtained for phase oscillators can be extended tophase-coherent chaotic systems. Finally, we carry out a series of experimentswith nonlinear electronic circuits to show the robustness of the theoreticalpredictions despite the intrinsic noise and parameter mismatch of theelectronic components.
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机译：我们研究了一组混沌振荡器的固有频率与它们所嵌入的网络的拓扑特性之间是否存在最佳相互作用。我们确定了以最有效的方式（即，以最低的耦合强度）实现相位同步的条件。具体而言，我们通过数值和实验结果表明，可以定义一个同步对齐函数，该函数将一组不相同的相干混沌振荡器的固有频率与拉普拉斯矩阵$ L $的拓扑联系起来，后者考虑了特定的振荡器之间相互作用网络的组织。我们使用经典的R'“ ossler系统来证明，可以将相位振荡器获得的同步对准函数扩展到相干混沌系统。最后，我们进行了一系列非线性电子电路实验，以证明尽管有内在因素，理论预测的鲁棒性电子元件的噪声和参数不匹配。
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