Because one of the main applications of chaos synchronization is oriented to data encryption and random number generators, fractional-order chaotic systems showing multi-scroll attractors have pointed out as feasible solutions to improve the performance of secure communications schemes. Nowadays, recent works have reported the analysis and control of fractional-order synchronization schemes for multi-scroll chaotic systems. However, the synchronization schemes from those works present mostly theoretical numerical simulations and give circuit simulations employing a simulator software rather than physical implementations. That way, our first contribution is to describe herein the experimental realization of a synchronization scheme for a fractional-order multi-scroll chaotic oscillator with a 4-scroll attractor and fractional-order $q=0.9$. First, we implemented the multi-scroll systems using an opamp-based analog circuit and an RC-based fractance device to emulate a fractional-order integrator. As a second contribution, we analytically demonstrate the complete synchronization between two identical multi-scroll systems employing two fractional-order controllers and the fractional-order derivative in the Caputo sense. By utilizing the Laplace transform theory, we analyze the one-way coupling method where the response (slave) system’s behavior depends on an identical drive (master) system. As a third contribution, we propose a passivity-based synchronization controller. This synchronization strategy consists of designing a virtual state feedback input and then based on the fractional-order Lyapunov theory, a control law obtains by designing an appropriate storage function to stabilize the system around its stable zero equilibrium. The experimental measures of the implemented synchronization scheme present suitable results compared to analytical and numerical findings.

由于混沌同步的主要应用之一是面向数据加密和随机数生成器，因此显示多滚动吸引子的分数阶混沌系统已被指出是提高安全通信方案性能的可行解决方案。现在，最近的工作已经报道了多滚动混沌系统的分数阶同步方案的分析和控制。然而，这些工作的同步方案主要是理论数值模拟，并给出采用模拟器软件而不是物理实现的电路模拟。这样，我们的第一个贡献是在此描述具有 4 滚动吸引子和分数阶的分数阶多滚动混沌振荡器的同步方案的实验实现$q=0.9$. 首先，我们使用基于运算放大器的模拟电路和基于 RC 的分形器件来模拟分数阶积分器来实现多滚动系统。作为第二个贡献，我们分析证明了使用两个分数阶控制器和 Caputo 意义上的分数阶导数的两个相同多卷轴系统之间的完全同步。利用拉普拉斯变换理论，我们分析了响应（从）系统的行为取决于相同的驱动（主）系统的单向耦合方法。作为第三个贡献，我们提出了一种基于被动的同步控制器。这种同步策略包括设计一个虚拟状态反馈输入，然后基于分数阶李雅普诺夫理论，通过设计适当的存储函数来使系统稳定在其稳定零平衡附近，从而获得控制律。与分析和数值结果相比，所实施的同步方案的实验措施呈现出合适的结果。