Dong Yujiao, Wang Guangyi, Iu Herbert Ho-Ching, Chen Guanrong, Chen Long
Institute of Modern Circuit and Intelligent Information, Hangzhou Dianzi University, Hangzhou 310018, China.
School of Electrical, Electronic, and Computer Engineering, The University of Western Australia, Perth, WA 6009, Australia.
Chaos. 2020 Oct;30(10):103123. doi: 10.1063/5.0002061.
This paper presents a chaotic circuit based on a nonvolatile locally active memristor model, with non-volatility and local activity verified by the power-off plot and the DC V-I plot, respectively. It is shown that the memristor-based circuit has no equilibrium with appropriate parameter values and can exhibit three hidden coexisting heterogeneous attractors including point attractors, periodic attractors, and chaotic attractors. As is well known, for a hidden attractor, its attraction basin does not intersect with any small neighborhood of any unstable equilibrium. However, it is found that some attractors of this circuit can be excited from an unstable equilibrium in the locally active region of the memristor, meaning that its basin of attraction intersects with neighborhoods of an unstable equilibrium of the locally active memristor. Furthermore, with another set of parameter values, the circuit possesses three equilibria and can generate self-excited chaotic attractors. Theoretical and simulated analyses both demonstrate that the local activity and an unstable equilibrium of the memristor are two reasons for generating hidden attractors by the circuit. This chaotic circuit is implemented in a digital signal processing circuit experiment to verify the theoretical analysis and numerical simulations.
本文提出了一种基于非易失性局部有源忆阻器模型的混沌电路，分别通过断电图和直流伏安特性图验证了其非易失性和局部活性。结果表明，基于忆阻器的电路在适当的参数值下没有平衡点，并且可以呈现出三种隐藏的共存异质吸引子，包括点吸引子、周期吸引子和混沌吸引子。众所周知，对于一个隐藏吸引子，其吸引盆与任何不稳定平衡点的任何小邻域都不相交。然而，发现该电路的一些吸引子可以从忆阻器局部有源区域的一个不稳定平衡点激发，这意味着其吸引盆与局部有源忆阻器的一个不稳定平衡点的邻域相交。此外，对于另一组参数值，该电路具有三个平衡点并且可以产生自激混沌吸引子。理论分析和仿真分析均表明，忆阻器的局部活性和一个不稳定平衡点是该电路产生隐藏吸引子的两个原因。该混沌电路在数字信号处理电路实验中实现，以验证理论分析和数值模拟。
