Stability Research On Hybrid Neural Networks

As a specific type of dynamic system,the neural dynamical system simulates the structure and function of real biological neurons and has extensive applications in various fields such as biology,physics,and economics.These applications all rely on the dynamic characteristics of the system.Therefore,the study of the dynamic properties of neural dynamical systems is of theoretical and practical significance.This thesis mainly studies several types of neural dynamical systems,and analyzes their dynamic evolution characteristics by using principles of contraction mapping,generalized Gronwall inequality,generalized It(?) formula,and inequality techniques,combined with specific systems.The related theoretical judgments are obtained.The main work of this thesis is summarized as follows:Firstly,a new type of delay differential algebraic complex-valued neural network is studied,and the existence and uniqueness of the solution to the system are discussed.The global index stability theorem of the system is also presented.In particular,it is not required that the activation function needs to separate the real part and the imaginary part.Secondly,a new highly nonlinear hybrid random neural network with variable delays is studied.It is usually unstable,and the network coefficients grow polynomially,which is different from the linear growth considered earlier.Due to the instability of the original system,a variable delay feedback control function is constructed to stabilize the controlled system.Finally,on the basis of the previous chapter,the case with neutral terms is considered,which is also unstable.Similarly,a variable delay feedback control function is established to maintain the stability of the controlled system.Four results of stable controlled systems are given respectively,and relevant criteria are formulated.