Dynamics Of Delayed Quaternion Neural Networks With Applications

Artificial neural network(ANN)is the basis of deep learning.In recent years,it has shown wider application prospects in image processing,associative memory and other fields.Considering the characteristics of real biological neurons,due to the speed limit of propagation,capacity limit in series system,especially the limited switching speed and transmission speed of neuronal amplifiers in neural networks,the delay is inevitable.Therefore,the study of timedelay neural networks is very necessary and meaningful.Because of the high storage capacity and the high efficiency in processing high-dimensional data of quaternion valued compared with real value and complex value.Consequently,quaternion valued neural networks have better theoretical and application prospects.In this paper,we study the global exponential synchronization characteristics under random impulses intensity and a class of global finite-time stability of the time-varying delay quaternion neural network model.Finally,the associative memory performance of quaternion neural networks with fixed time delay is considered.The specific contents are as follows:1.Two kinds of synchronization problem of quaternion valued neural networks are studied.Firstly,the global exponential synchronization problem of a class of delayed quaternion neural networks with stochastic impulses is considered,in which the trigger time and intensity of the impulses are all random.Based on the equivalent real number error system of quaternion valued error model,combined with the expected form of Lyapunov function Dini-derivative,using the comparison principle and fallacy reduction method,a new LMI criterion with no delay dependence for global exponential synchronization is obtained.Second also based on the equivalence of the real valued system without time delay,we use a series of definite integral,variable replacement and inequality techniques,established a new fixed-time stability theorem,finally studies the quaternion valued neural networks master-slave system under a given controller in fixed-time synchronization,as well as get the more precise setting moment.2.Based on the extended Lyapunov-Razumikhin(L-R)method,the global finite-time stability of quaternion valued neural networks with time-varying delays is studied,and a new upper bound estimate of the convergence rate of the system solution is obtained.Firstly,an extended lemma is proposed to make the original system achieve the global finite-time stability by constructing L-R functionals satisfying two specific inequality conditions,which solves the difficult problem to find suitable Lyapunov functionals for general global finite-time stability problems.Then,the global finite-time stability of the system is achieved and a new upper bound estimate of the convergence rate of the system solution is obtained by means of an appropriate controller and the equivalent L-R method for the real-valued system.3.We studied the asymptotic stability of the equilibrium point of a semi-discretized timedelayed quaternion valued neural network in continuous time and the parameter design of the discretized model to store the specified state vector.Firstly,the corresponding discretized network model is obtained by semi-discretization for the continuous time-delay quaternion valued system.For a given state that needs to be stored,we set it as the equilibrium point of the system in two different ways,and obtain the corresponding network model parameters by different algorithm steps.The stability of the set network equilibrium point is analyzed,and some conditions for determining the asymptotic stability of the system are obtained.Meanwhile,the correctness of the designed network parameters is verified.