Dynamic Analysis Of Memristor-based Recurrent Neural Networks

Within the architecture of traditional computer, information memory and processing are separate. The delivery channels of information memory and processing are connected via bus, which will be hard to break "Von Neumann challenge", severely restricting the ad-vancement of high performance computing. However, the combination is that of information memory and processing for human brain, due to the synaptic plasticity. Therefore, devel-oping new memory devices with storage and processing, in order to support the computing architecture of information storage and fusion processor, may be potential future directions for the next generation ultra-high-performance computing. As a new memory device, the features of memristor most closely resemble cerebral synapses. It is believed that memristor may achieve integrated function of information memory and processing, similar to cerebral synapses, giving a new design scheme for new-type computer architecture that can break through the "Von Neumann challenge"Memristive neural systems made of hybrid complementary metal oxide semiconduc-tor array structure have demonstrated the superior capabilities in the resistance changing memory, super-speed, low-power dissipation, high integration density, etc, which can form a basis for the realization of powerful brain-like "neural" computer. This neuromorphic electronic system can enable data storage and to achieve logic operation, which may make great breakthrough in the respect of blending of information memory and processing, and lay a good foundation for structuring new-type computer architecture. Nevertheless, some significant problems in nonlinear system theory based on memristive neural systems remain to be resolved. Exploring the evolving dynamic mechanism of memristive neural systems will contribute to regulate the threshold stimulating function of neurons, which can provide basic theory support to information memory and processing based on memristor, and breed lots of major opportunities for storage and computation on dynamic information.The dissertation focuses on memristive neurodynamic systems. Several classes of memristor-based recurrent neural networks are formulated and studied. Some preliminary theoretic principles on dynamic behaviors of these networks are derived. The analysis in the dissertation employs results from the theory of discontinuous dynamical systems, linear matrix inequalities and mathematical analysis techniques. An interesting theoretical result of this research work is that the memristive systems can be cleverly analyzed according to the theories of differential inclusions and set-valued maps. The main contents are sketched out as follows: The basic theories of dynamics on memristor-based recurrent neural networks are dis-cussed. By means of structuring a class of memristor-based Lotka-Volterra neural networks and a class of memristor-based neural networks with various feedback functions, within mathematical framework of the Filippov solution, the attractivity, complete stability of memristor-based Lotka-Volterra neural networks, and the Lagrange stability of memristor-based neural networks with various feedback functions are analyzed, respectively. These results can be applied to the memristive dynamic memories. The theoretical analysis can characterize the fundamental electrical properties of memristor devices and provide conve-nience for applications.The control design of memristor-based recurrent neural networks is studied. By intro-ducing a class of memristor-based multi-model neural networks, the exponential stabiliza-tion and optimal control are presented. The obtained results can be applied to the closed-loop control of memristive systems. These analytical results were the improvement and extension of the existing results in the literature.The application of dynamics on memristor-based recurrent neural networks is inves-tigated. Combining with a class of memristor-based linear threshold neural networks, the pattern memory analysis is established by using local inhibition and local invariant sets. The derived results extend some previous works on pattern memory analysis of conventional re-current neural networks.The study on dynamic analysis of memristive neurodynamic systems will be helpful in approaching nanoscale charge transport mechanisms of this new electronic information system, and making more explicit mechanisms on information storage and computing based on memristor. Such a study also sets the base and tone for the future development of high performance electronic storage systems that can realize integration of information memory and processing.