Almost Periodic Solutions And Synchronization Problem Of Memristive Neural Networks

As a new generation of neural network, memristive neural network has many new dynamic properties which are very different from those of traditional neural network. On the other hand, there are many types of memristive ANN in terms of character and state. So lots of new problems are to be solved, including some traditional problems, which ensures the substantial development of theory research and practical application of memristive neural network.Widely based on large numbers of related documents and by applying differential inclusion, Lyapunov method and linear matrix inequality techniques, this paper has studied memristive neural network deeply. The main works are listed as follows:Firstly, the existence of overall solution of memristive neural networks with mixed time-varying delays and that this overall solution is of gradually almost periodic were proofed by applying differential inclusion and Lyapunov method. And then the existence of almost periodic solution of this model was proofed by using Lebesgue convergence theorem. Sufficient conditions for the existence of periodic solution of memristive neural networks with constant time-varying delays were provided.Secondly, an adaptive controller was designed, by which infinite time completely periodic synchronization of a master system and a slave system was realized. Feasibility of this synchronization was proofed by applying linear matrix inequality techniques. The easily testable finite-time complete synchronization criteria have been obtained to ensure the synchronization goal, hence the results obtained in this paper are easily applied in practice engineering.At last, simulations based on MATLAB for all the results obtained in this paper on almost periodic solutions and synchronization were performed, which indicated that conclusions obtained are right.