忆阻电路复杂振荡的几何与分布调控研究

Memristive circuit has attracted great interests for the reason that its complex oscillation behaviors including chaos and multistability demonstrate tremendous application in chaotic secure communication and circuit information storage; however, an effective method for regulating and controlling the complex oscillation in memristive circuits hasn’t been found. The present study indicates that in chaotic systems non-bifurcation parameters can control the amplitude and offset of chaotic signials, and that attractor reproducing can be realized based on offset boosting. Memristive circuit as a special nonlinear system has the similar property of amplitude control and offset boosting. This project aims to solve the issue of regulating and controlling chaotic oscillation in memristive system with different memristor models. Through the analysis of the degree distribution and variable-dependence relation according to the characteristics of nonlinear functions, a new method for controlling the size and position of the attractor will be constructed based on non-bifurcation parameter; by means of revising the balance of polarity or introducing offset modulation function, a new structure of conditional symmetry can be constructed in memristive systems or a new type of self-reproducing system can be coined which output pairs or lattice of coexisting attractors. Based on the above exploration, further joint regulation and control of the memristive oscillation can be achieved including geometric regulation and multi-attractor distribution control in physical memristive circuit with memristor chip or equivalent unit. The exploration of this project can not only reveal the regulation mechanism of the oscillations in memristive circuits theoretically, but also puts forward a set of methods for attractor control which can promote the application of the memristive circuit.

忆阻电路中混沌和多稳态复杂振荡行为在混沌保密通信和电路信息储存方面具有极大的应用价值从而引起了广泛的兴趣。然而，目前尚未发现忆阻系统混沌振荡的有效调控方法。经研究发现：混沌系统存在非分岔参数能实现混沌信号的幅度与偏置控制；基于偏置思想可实现吸引子繁衍。忆阻电路作为一种特殊非线性系统，其复杂振荡行为可得到类似的调控。本项目研究包含不同忆阻模型的忆阻系统的混沌振荡调控问题，通过对系统反馈项次数和反馈变量的分布特征分析，建立一种基于非分岔参数的吸引子大小与位置调控方法；通过改变极性平衡关系或引入偏置控制函数，构建条件对称或自繁衍忆阻系统使之输出成对吸引子流或者网格多吸引子；引入实际忆阻器件或采用忆阻等效单元设计忆阻电路实现混沌的几何调控和吸引子分布调控，在此基础上进一步实现忆阻振荡的联合调控。本项目不仅在理论上揭示忆阻电路振荡的调控机理，提出的一整套吸引子调控方法更有助于推动忆阻电路的应用。

项目主要研究忆阻混沌振荡的几何调控与分布调控。通过忆阻器变量约束和动力系统拓扑的设计，在忆阻系统中内置调幅、调偏置参数。基于变量偏置与反馈函数选择，在忆阻系统相空间中繁衍更多的共存吸引子，并对吸引子实施分布调控。构建忆阻实验平台，实现混沌振荡的调控，基于此提升应用系统的性能。研究得到如下结论。.1.忆阻振荡幅度调控。忆阻器的磁通与电荷约束关系和系统拓扑结构的选择可实现幅度控制。一般情况下，引入绝对值忆阻能实现局部调幅，在Jerk系统结构中引入平方项或者高次项忆阻可实现全局调幅，在幅频同调系统结构中引入绝对值忆阻可保持幅频同调。保守系统及耗散系统都可实现混沌调控。.2.忆阻振荡偏置调控。系统拓扑对于偏置调控具有更直接的影响，偏置可控系统中可提取忆阻器约束关系而保留偏置控制功能。耗散系统引入忆阻器可转变为保守，此时固定初值的偏置控制将触发不同共存振荡。四维或者高维系统可引入更多的忆阻器而保留偏置调控功能。.3.多吸引子繁衍与分布调控。动力学系统的偏置控制可作为吸引子繁衍的入口。基于偏置控制，引入绝对值函数可实现条件对称，输出一对吸引子；代入绝对值函数结合符号函数极性补偿可实现吸引子倍增；引入周期函数可实现吸引子自繁衍甚至形成吸引子生长，多维自繁衍将输出网格吸引子，脉冲函数与周期函数结合可选择吸引子数量和种类；参数空间的吸引子可借助分段线性函数转泊到初值空间，实现动力学编辑。.4.可调控忆阻电路实现与应用系统设计。对乘法器等非线性器件的功能复用，结合分立电子器件可进一步简化忆阻系统的电路实现，引入忆阻器可实现神经元网络的动力学调控，而可调控离散混沌映射能够输出更多可控混沌序列，可用来改善图像加密和伪随机数发生器的性能。.如上发现进一步丰富了动力学系统的调控与多稳态理论，拓展了忆阻器在混沌电路和忆阻神经动力系统中的应用空间，也为忆阻集成应用电路的设计提供了重要参考。