Experimental datasets on intermittency in networks of electronic oscillators. Hybrid Configuration - Random (Erdös-Rényi) Topology

For experimental validation, we developed a real-time hybrid implementation of a coupled oscillator network. The system consists of a network of $N=28$ oscillators, whose dynamics are governed by the Rössler-like system of equations. The procesing of all $N$ signal of the electronic oscillators for constructing and coupling the network were executed in real-time on a National Instruments CompactRIO (cRIO-9074) embedded control and acquisition platform. The cRIO platform was programmed to perform the real-time operations required to process the oscillator states and generate the corresponding coupling signals based on a predefined adjacency matrix, $A$. This flexible architecture allowed us to systematically investigate network topologies; in this case: Random (Erdös-Rényi). The "hybrid" nature of the implementation refers to the control of the global coupling parameter, $d$. This parameter was not set digitally but was controlled via an analog DC voltage provided by an external, automated power supply. This setup enabled precise and repeatable experimental sweeps of the coupling strength In general, the cRIO was configured to continuously acquire the analogic outputs of each $N$ oscillators, compute the synchronization coupling signal according to the Laplacian network topology $L$, and subsequently introduce in the $N$ oscillator the corresponding feedback signals to the system. The global coupling strength, $d$, was externally regulated via an analog voltage supplied by a GW-Instek GPD-2030S programmable power supply. This voltage was varied within the range of 0 V to 3.5 V. This range was empirically determined to be necessary to observe the complete route to synchronization, which was scanned in 701 discrete steps ($delta = 0.005$). Furthermore, to prevent signal saturation in the feedback loop, a scaling gain of $\psi = 0.1$ was applied to the coupling signal.为开展实验验证，我们构建了耦合振子网络的实时混合实现方案。该系统包含N=28个振子组成的网络，其动力学行为由类罗斯勒（Rössler）方程组控制。 用于构建与耦合该网络的全部N个电子振子信号的处理过程，均在美国国家仪器（National Instruments）CompactRIO（cRIO-9074）嵌入式控制与采集平台上实时完成。 该cRIO平台经编程后可执行所需的实时操作：处理振子状态，并基于预定义的邻接矩阵A生成对应的耦合信号。此灵活架构支持我们系统性地探究网络拓扑结构，本次实验采用的拓扑为随机（Erdös-Rényi）网络。 本实现方案的“混合”特性体现在全局耦合参数d的控制方式上：该参数并非通过数字方式设定，而是由外部自动化电源提供的模拟直流电压进行调控。此实验装置可实现耦合强度的精准且可重复的扫描测量。 总体而言，该cRIO平台经配置后可持续采集全部N个振子的模拟输出信号，依据拉普拉斯（Laplacian）网络拓扑L计算同步耦合信号，并将对应的反馈信号注入至N个振子系统中。 全局耦合强度d由GW-Instek GPD-2030S可编程电源提供的模拟电压进行外部调控。该电压的调节范围为0 V至3.5 V，此范围经实验确定为观测完整同步路径所必需，本次实验以701个离散步长进行扫描（步长Δ=0.005）。此外，为避免反馈环路中出现信号饱和，我们对耦合信号施加了ψ=0.1的缩放增益。