忆阻电路的复杂动力学与多稳定状态控制策略研究

Memristor based chaotic ocsillating circuits and neuromorphic circuits have complex dynamics including multistability, extreme multistability, and so on. Revealing complex dynamics and constructing multi-steady-state control strategy are the key problems which need to be solved in engineering applications of memristive circuits. However, basic theories are not mature enough and many problems still require for further study. Focusing on the key problems methioned above, the following main research contents are performed in this project. 1. Some novel memristor emulators are proposed, upon which various memristor based application circuits including chaotic oscillating circuits and neuromorphic circuits are synthesized. 2. Bifurcation behaviors with the variations of the parameters for self-excited or hidden oscillations in the memristive circuits are studied, coexisting phenomena of multiple attractors or infinitely many attractors and their forming mechanisms are revealed and resoved, multi-scale effects are explored, and bursting phenomena and their induced mechanisms in fast-slow sub-structures are elaborated. 3. Extreme multistability in the memristive circuits with line, plane, or space equilibrium points is investigated, spatial orientations for initial states of attractor attraction basins are carried out, a transformation method converting multi-steady-state into system-parameter is proposed, and multi-steady-state control strategy for the memristive circuits is constructed to develop their potential applications in the field of image processing and compressed sensing. Finally, some analysis methods and experiment means for the memristive circuits are built, and memristive circuit network theory is thereby developed and improved to provide theorectical guidance for engineering applications.

基于忆阻的混沌振荡电路和神经形态电路具有多稳定性或超级多稳定性等复杂动力学。揭示复杂动力学并构建多稳定状态控制策略是忆阻电路工程应用必须解决的关键问题。然而，基础理论还不够成熟，尚待研究的问题还很多。针对上述关键问题，本项目开展如下主要研究内容。1.提出若干新颖忆阻模拟器，综合设计多种基于忆阻的混沌振荡电路和神经形态电路等应用电路；2.研究忆阻电路随参数变化的自激或隐藏振荡的分岔行为，揭示并解析多吸引子或无限多吸引子的共存现象及其形成机理，探索多尺度效应并阐述快慢子结构下的簇发现象及其诱发机制；3.研究具有线、面或空间平衡点忆阻电路的超级多稳定性，进行吸引子吸引盆的初始状态空间定位，提出多稳定状态-系统参数变换法，构建忆阻电路的多稳定状态控制策略，拓展在图像处理和压缩感知等领域的潜在应用。最终建立忆阻电路的若干分析方法和实验手段，发展并完善忆阻电网络理论，为工程应用提供理论指导。

作为电网络理论的第四种电路元件，忆阻器有着天然的非线性和可塑性，与其它电路元件有机组合，容易构建出基于忆阻的混沌振荡电路和神经形态电路等应用电路。然而，基于忆阻的各种应用电路研究是近几年才逐步开展的，基础理论还不够完善，尚待研究的问题还很多。因此，需要进一步发展和完善忆阻电网络理论，探讨忆阻的非线性在混沌振荡电路复杂动力学与形成机理方面的作用，揭示忆阻的可塑性在神经网络及神经形态电路演化与功能方面的意义，并针对应用背景综合设计多种新颖忆阻电路，进而积极推动这类电路在信息科学与计算神经科学等各个领域的应用。. 已结题项目“忆阻电路的复杂动力学与多稳定状态控制策略研究”，在忆阻模拟器及其混沌振荡电路和神经形态电路，忆阻电路复杂动力学的现象揭示、机理分析与实验验证，以及忆阻电路超级多稳定性与多稳定状态控制策略等方面进行了深入研究。项目主要成果如下： . ▲提出了一类忆阻模拟器，构建了若干基于忆阻的非线性系统与神经元网络，揭示了忆阻电路的超级多稳定性、初值位移调控、放电模态转迁等复杂非线性现象，并基于模拟与数字电路进行了硬件电路实现与实验验证。. ▲针对伏安模型理论分析瓶颈，提出了忆阻电路的增量韦库建模理论，实现了多稳定性的降维重构、机理演绎和硬件控制；进而提出了增量积分建模理论，解析了基于忆阻的非线性系统与神经元网络的多稳定性形成机理。. ▲揭示了忆阻神经元网络的共存放电模态和尖峰/簇放电模态转迁等动力学行为，解析了随参数扰动与初值演化时放电活动的分岔机理，并研究了忆阻电磁感应对神经元网络放电活动的动力学效应及其诱发机制。.此外，初步探讨了忆阻连续模型的离散建模思路，开展了从连续时间域拓展至离散时间域的忆阻建模研究，揭示了忆阻在离散系统中的混沌复杂性强化效应，并开展了基于混沌的工程应用研究，取得了部分先期研究成果。