The Global Stability And Periodicity Of A Few Class Of Recursive Neural Network With Proportion Delay

Neural networks with delays are widely used in image processing, pattern recognition and other fields, in these applications it usually require a equilibrium point which is stable, so the stability of a class of recursive neural network time-delay research has important theoretical and practical significance. Proportional delay is a kind of unbounded time-varying delay which is different from constant delay, bounded time-varying delay and distributed delay. Proportion time-delay systems, as a kind of important mathematical models, play an important role in physics systems, biological systems, control theory, and other fields. In this paper, the stability and periodicity of a few class of recursive neural network with proportion delay is studied.The first chapter introduces the research background and development history of the neural network, the recursive neural network, the research present situation of the recursive neural network stability and the main work of this article.The second chapter, the global asymptotic stability of a class of recursive neural network with proportion delay is studied based on LMI. Through constructing a suitable Lyapunov functional and using the linear matrix inequality (LMI), get a stability criterion based on LMI.The third chapter studies the global asymptotic stability of a class of neutral recursive neural network with proportion delay. Through constructing a suitable Lyapunov functional and using matrix Schur complement nature, get a stability criterion based on matrix eigenvalue.The fourth chapter studies the global exponential periodicity of a class of recursive neural network with proportion delay. Through constructing proper Lyapunov functionals and applying contraction mapping theory and fixed point theorem, studied the global exponential periodicity of the system, some sufficient conditions are derived for ensuring the existence and uniqueness of the periodic solutions and global exponential periodicity.Each chapter gives out specific numerical examples, and simulations of the results, and verify the correctness and effectiveness of the obtained results.