Polynomial Stability Of Several Classes Of Multi-proportional Time-delay Neural Networks And Their Applications

Time delay,caused by finite switches of amplifiers,is objective and inevitable during the process of running neural networks.In other words,the state of neural networks not only depends on the current state of neurons,but also on the past state of neurons.Therefore,considering delayed neural networks can better reflect the real situations and has more practical significance.As a kind of unbounded time delay,proportional delay is different from constant time delay,bounded timevarying delay and distributed time delay.Proportional delayed neural networks have important applications in security communication and image encryption and decryption.This article mainly discusses polynomial stability of several kinds of multi-proportional delayed neural networks and the application of proportional delayed neural network in quadratic programming problem.In the first chapter,we introduce the history of neural networks.Subsequently,the research status of stability and their applications are presented,involving non-proportional and proportional delayed neural networks.In the second chapter,stabilities of the multi-proportional delayed neural network with impulse are discussed.New criteria about globally asymptotic stability and polynomial stability of the neural network are acquired by designing two new Lyapunov functions and applying inequality techniques.Numerical examples and imitated diagrams show the results are effective.In the third chapter,exponential stability and polynomial stability of the inertial neural network with multi-proportional delays are analyzed.Firstly,we declare the equilibrium point is available and unique based on Brouwer’s fixed point theorem and reduction to absurdity.Moreover,by designing delay differential inequalities and applying Lagrange’s mean value theorem as well as norm properties,globally exponential stability about the network can be obtained,and then the polynomial stability are acquired by utilizing the method of variable substitution.Finally,numerical experiments are provided to demonstrate the theoretical results are correct.In the fourth chapter,the optimal solution of the quadratic programming problem with equality constraints is transformed into the proving of existence of the stable equilibrium point for a class of proportional delayed projection neural network by utilizing variational inequality.We firstly prove the proportional delayed neural network exists unique equilibrium point by applying homeomorphism mapping principle.Simultaneously,delay-dependent criteria about global exponential stability and global polynomial stability are also acquired by applying inequality techniques and the method of variation of constants.Finally,criteria are successfully applied to solve the quadratic programming problem.A numerical example demonstrate that,compared with the proportional delayed Lagrange neural network,the proportional delayed projection neural network is faster in terms of convergence rate.The conclusions achieved by this paper are original,logical and verifiable.The correctness and effectivity of the results in each chapter can be verified by numerical experiments and corresponding imitated diagrams.These results in this paper lay a theoretical foundation for applications of proportional delayed neural network.