School of Electronics and Information, Guangdong Polytechnic Normal University, Guangzhou 510665, China.
School of Automation, Guangdong Polytechnic Normal University, Guangzhou 510665, China.
Chaos. 2023 Jan;33(1):013141. doi: 10.1063/5.0124793.
Fractional-order systems generalize classical differential systems and have empirically shown to achieve fine-grain modeling of the temporal dynamics and frequency responses of certain real-world phenomena. Although the study of integer-order memory element (mem-element) emulators has persisted for several years, the study of fractional-order mem-elements has received little attention. To promote the study of the characteristics and applications of mem-element systems in fractional calculus and memory systems, a novel universal fractional-order mem-elements interface for constructing three types of fractional-order mem-element emulators is proposed in this paper. With the same circuit topology, the floating fractional-order memristor, the fractional-order memcapacitor, and fractional-order meminductor emulators can be implemented by simply combining the impedances of different passive elements. PSPICE circuit simulation and printed circuit board hardware experiments validate the dynamical behaviors and effectiveness of our proposed emulators. In addition, the dynamic relationship between fractional-order parameters and values of fractional-order impedance is explored in MATLAB simulation. The proposed fractional-order mem-element emulators built based on the universal interface are constructed with a small number of active and passive elements, which not only reduces the cost but also promotes the development of fractional-order mem-element emulators and application research for the future.
分数阶系统推广了经典微分系统，并在经验上证明了它们可以实现对某些实际现象的时间动态和频率响应进行细粒度建模。尽管整数阶记忆元件（mem-element）仿真器的研究已经持续了多年，但分数阶 mem-element 的研究却很少受到关注。为了促进分数微积分和记忆系统中 mem-element 系统的特性和应用研究，本文提出了一种新颖的通用分数阶 mem-element 接口，用于构建三种类型的分数阶 mem-element 仿真器。通过相同的电路拓扑，只需组合不同无源元件的阻抗，就可以实现浮动分数阶忆阻器、分数阶忆容器和分数阶忆感器仿真器。PSPICE 电路仿真和印刷电路板硬件实验验证了我们提出的仿真器的动态行为和有效性。此外，在 MATLAB 仿真中还探讨了分数阶参数与分数阶阻抗值之间的动态关系。基于通用接口构建的所提出的分数阶 mem-element 仿真器使用少量的有源和无源元件构建，不仅降低了成本，而且还促进了分数阶 mem-element 仿真器的发展和未来的应用研究。
