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。

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.