Ma Jun, Zhou Ping, Ahmad Bashir, Ren Guodong, Wang Chunni
School of Science, Chongqing University of Posts and Telecommunications, Chongqing, China.
Department of Physics, Lanzhou University of Technology, Lanzhou, China.
PLoS One. 2018 Jan 17;13(1):e0191120. doi: 10.1371/journal.pone.0191120. eCollection 2018.
In this paper, a new four-variable dynamical system is proposed to set chaotic circuit composed of memristor and Josephson junction, and the dependence of chaotic behaviors on nonlinearity is investigated. A magnetic flux-controlled memristor is used to couple with the RCL-shunted junction circuit, and the dynamical behaviors can be modulated by changing the coupling intensity between the memristor and the RCL-shunted junction. Bifurcation diagram and Lyapunov exponent are calculated to confirm the emergence of chaos in the improved dynamical system. The outputs and dynamical behaviors can be controlled by the initial setting and external stimulus as well. As a result, chaos can be suppressed and spiking occurs in the sampled outputs under negative feedback, while applying positive feedback type via memristor can be effective to trigger chaos. Furthermore, it is found that the number of multi-attractors in the Jerk circuit can be modulated when memristor coupling is applied on the circuit. These results indicate that memristor coupling can be effective to control chaotic circuits and it is also useful to reproduce dynamical behaviors for neuronal activities.
本文提出了一种新的四变量动力学系统，用于构建由忆阻器和约瑟夫森结组成的混沌电路，并研究混沌行为对非线性的依赖性。采用磁通量控制忆阻器与RCL并联结电路耦合，通过改变忆阻器与RCL并联结之间的耦合强度来调制动力学行为。计算分岔图和李雅普诺夫指数，以确认改进后的动力学系统中混沌的出现。输出和动力学行为也可以通过初始设置和外部刺激来控制。结果表明，在负反馈下，混沌可以被抑制，采样输出中会出现尖峰，而通过忆阻器应用正反馈类型可以有效地触发混沌。此外，研究发现，当在电路上应用忆阻器耦合时，可以调制Jerk电路中的多吸引子数量。这些结果表明，忆阻器耦合可以有效地控制混沌电路，并且对于再现神经元活动的动力学行为也很有用。
