The Research For Existence Of Periodic Solutions For Neutral-type Neural Networks

It is well known that the problem of existence of periodic solutions is an importantproblem in for neutral-type Neural Networks, and its research results have been extensivelyapplied in many diferent areas, and especially, it has important signifcance in automaticcontrol, signal and image processing, pattern recognition and optimization etc. However,along with the progress and development of the society, we need to study neural networkof periodic solutions more detailed. In this paper, a class of neutral neural networkswith distributed delays and a class of neutral type Cohen-Grossberg neural networks withtime-varying delays are investigated by applying abstract continuation theorem of k-setcontractive operator, some sufcient criteria are derived to ensure the existence of periodicsolution of the addressed neural networks with neutral delays.The main contents in this paper can be summarized as follows:The frst chapter, the research background, purpose and signifcance of neural networkare introduced, and describe the research situation of periodic solutions. After that, theorganization of this paper is given.The second chapter, the defnition of k-set contractive, abstract continuation theoremof k-set contractive operator are introduced. To lay the foundation for the back of thetheoretical analysis.The third chapter, a class of neutral neural networks with distributed delays is in-vestigated, some sufcient criteria are derived to ensure the existence of periodic solutionof the addressed neural networks with neutral delays. Numerical simulation verify theexistence of periodic solution is correct and efective.The fourth chapter, a class of neutral type Cohen-Grossberg neural networks withtime-varying delays are investigated, some sufcient criteria are derived to ensure theexistence of periodic solution of the addressed neural networks with neutral delays. The- oretic proof and numerical simulation verify the efectiveness and correctness of proposedmethod.The ffth chapter, we make a conclusion on the whole work. By the comparison ofthe old results, It is shown that this article of study method is an more efective numericalmethod.