Chang Hui, Song Qinghai, Li Yuxia, Wang Zhen, Chen Guanrong
College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China.
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China.
Entropy (Basel). 2019 Apr 19;21(4):415. doi: 10.3390/e21040415.
This paper reports the finding of unstable limit cycles and singular attractors in a two-dimensional dynamical system consisting of an inductor and a bistable bi-local active memristor. Inspired by the idea of nested intervals theorem, a new programmable scheme for finding unstable limit cycles is proposed, and its feasibility is verified by numerical simulations. The unstable limit cycles and their evolution laws in the memristor-based dynamic system are found from two subcritical Hopf bifurcation domains, which are subdomains of twin local activity domains of the memristor. Coexisting singular attractors are discovered in the twin local activity domains, apart from the two corresponding subcritical Hopf bifurcation domains. Of particular interest is the coexistence of a singular attractor and a period-2 or period-3 attractor, observed in numerical simulations.
本文报道了在一个由电感和双稳态双局部有源忆阻器组成的二维动力系统中发现的不稳定极限环和奇异吸引子。受区间套定理思想的启发，提出了一种寻找不稳定极限环的新的可编程方案，并通过数值模拟验证了其可行性。在忆阻器基动态系统中的不稳定极限环及其演化规律是从两个亚临界霍普夫分岔域中发现的，这两个域是忆阻器双局部活动域的子域。除了两个相应的亚临界霍普夫分岔域外，在双局部活动域中还发现了共存的奇异吸引子。特别值得关注的是，在数值模拟中观察到奇异吸引子与周期-2或周期-3吸引子的共存。
