Dynamic Analysis Of Several Kinds Of Differential-algebraic Neural Networks

Neural network is a kind of mathematical model which uses the structure similar to synaptic connection of brain to process information.Neural networks are widely used in pattern recognition,signal processing,knowledge engineering,robot control and other fields,and the important index to realize these applications is the dynamic behavior of the system.Therefore,it is of theoretical and practical significance to study the performance of the network in depth.This paper studies the neural network dynamics of several types of differential-algebraic equations.Using the theory of differential algebraic systems,integral Gronwall inequality,matrix inequality,Lipschitz condition,differential equation theory,etc,some specific dynamic models are analyzed and criteria for the characteristics of the neurodynamic system are obtained.The main works of this paper are summarized as follows:The evolutionary properties of a class of complex-valued memristive differential-algebraic neural networks are studied.Using multivalued differential median theorem and differential equation dynamic system control theory,effective conditions are provided to ensure the global asymptotic stability of the system.Based on the properties of nonsingular M-matrix and the definition of stability,some conditions for the existence and uniqueness of the equilibrium point of the model are given,and it is proved that the equilibrium point is globally asymptotically stable.This paper explores the synchronization control of a class of differential-algebraic recursive neural networks.By using the principles of centralized and decentralized data-sampling,based on the characteristics of differential-algebraic equations,the control conditions for the system to achieve out-synchronization are given.Criteria for excluding the Zeno phenomenon are also provided.The robust analysis of a class of recursive differential-algebraic neural networks with deviating argument and stochastic disturbance are discussed.By analyzing the relationship between the state variables with argument function and undisturbed,it is proved that the disturbed system also meets this property by taking advantages of the global exponential stability of undisturbed systems.The system with deviating argument and stochastic undisturbed achieves mean square stability.The above analysis of the system has provided numerical examples to prove the validity of the conclusions.