Synchronization And Stability Of Several Types Of Proportional Time-delay Neural Network

Relaying on superior fitting ability,parallel computing and distributed processing capabilities,neural networks is an integrated-multiple-fields interdisplinary,which integrates and plays a part in biology,control science,the intersection of information science and mathematics with crucial contribution to solve related complex problems in pattern recognition,image processing as well as medical diagnosis.Time delay is an inevitable phenomenon in the operation of neural networks,which originates from the inevitable delay in the switching of amplifiers and transmission signals in circuits.It can change the dynamic behavior of neural networks.Proportional delay is a kind of unbounded time-varying delay,whose existence causes neural networks to always be accompanied by increasing and varying delays.This context analyzed the global exponential synchronization,polynomial synchronization and finite-time synchronization of proportional delay neural networks.Additionally,exploring the proportional delay neural networks on solving quadratic programming problems.Major contents are as follows:The first chapter states the development history of neural networks briefly,and emphasis is laid on stating the research status of proportional delay neural networks and proportional delayed competitive neural networks,as well as the application of proportional delay neural networks.Take a simplification of non-proportional delay neural networks and its applications.The second chapter analyzes the synchronization of the multi-proportional delayed neutral competitive neural network with time-varying coefficients.Before all others,constitute delaydependent feedback controller.By constituting Lyapunov function,the assertions of global polynomial synchronization and finite-time synchronization are attained.Next,by the hand of numerical simulation,the truthfulness of theory results are verified.In end,show the specific application of synchronization in image encryption and decryption.The third chapter investigates the synchronization of proportional delayed fuzzy neutral competitive neural networks.For one thing,via long term memory and short term memory of system controlled method,the global exponential synchronization of system is analyzed by constructing a Lyapunov function.Then,via nonlinear transformation as well as the short term memory controlled method,designing a Lyapunov functional to research the global polynomial synchronization,obtaining the delay-dependent and delay-independent principles.In end,theory results are validated by numerical simulations.In the forth chapter,for a sort of quadratic programming problem on a close convex set,projection neural networks are constructed by Lagrange function and invariant inequality.The balance point of system is proved to be the solution of quadratic programming problem in terms of saddle point theorem.Based on nonlinear transformation,Lyapunov function method and quality of inner product,the global asymptotic stability of projection neural networks with proportional delay are analyzed and criteria of its are gained.Simulation results illustrate the effectiveness and practicability of results we gained.This paper analyzes the synchronization of two sorts of competitive neural networks with proportional delay and the stability of projected neural networks with proportional delay,research results are tested by numerical simulation results.This context provides theory support for further application on synchronization of proportional delayed neural networks.