Study On The Stability Of Complex-valued Neural Networks With Time Delay

Since Hirose A proposed the fully complex-valued neural networks which the state,output,weight and attraction domain are all complex-valued in 1992,various complex-valued neural networks have been proposed.The activation function,weight,output and state of the complex-valued neural networks neurons are all complex-valued,so the complex-valued neural networks can be regarded as an extension of real-valued neural networks.Consequently,the characteristics of the complex-valued neural networks are more complicated and excellent.It can directly process complex-valued data and solve many problems that real-valued neural networks cannot solve.In fact,since the complex-valued neural networks are nonlinear systems,time delay is inevitable in the process of system hardware operation.Therefore,the study of the dynamic behavior of the complex-valued neural networks with time delay has not only become a hot research field,but also attracted the interest of many scholars at home and abroad.To analyze the stability of complex-valued neural networks with time delays,it is necessary to select the appropriate activation function and the normal operation of a reasonable networks parameter system.After discussing and analyzing the stability of the complex-valued neural networks with time delays,the system can solve many problems in practical life.Therefore,it is of great significance to study the stability of complex-valued neural networks with time delays in depth.1 Boundedness and global exponential stability of complex-valued neural networkss with variable coefficients and proportional delaysThis chapter not only investigates the boundedness problem of complex-valued neural networks with variable coefficients and proportional delays,but also researches the global exponential stability of the system proposed.Instead of using the state variable transformation method in the existing literature,this chapter uses the method of mathematical analysis and the technique of inequality technology,a sufficient criterion for ensuring the boundedness and the global exponential stability of the proposed is derived.In particular,when the coefficient of the neural networks is constant,this is a special case of a complex-valued neural networks with variable coefficients and proportional delays.Sufficient criteria are also derived to guarantee the existence,uniqueness and global exponential stability of the equilibrium point.Finally,the numerical simulation of the example is obtained by applying MATLAB software,andnumerical examples show that the model tends to stabilize at t(28)2s,and the validity of the obtained results is verified.2 The boundedness and robust stability of delayed complex valued neural networks with interval parameter uncertainties For the delayed complex-valued neural networks with interval parameter uncertainties,the problems of boundedness and robust stability are learned.By using the homeomorphic mapping theorem,the inequality technique and the establishment of a reasonable Lyapunov function,the boundedness,existence,uniqueness and the robust stability of neural networks are derived.Then we give the linear matrix inequalities in complex-valued form,not only do not ignore the symbols of the connection weights in the networks,but also easily calculate the feasible solutions by using the calculators YALMIP and SDPT3 in the MATLAB software.Compared with the methods of other recent literature,this method in this chapter has less limitations.Finally,the simulation example shows that the model tends to be stable at t(28)10s,the validity and applicability of the conclusions obtained from the verification are verified.3 Impulsive control of financial system stabilityThis paper mainly studies the stability of impulsive financial system with time delay.Firstly,a delayed financial model with impulsive control is established.Then,in order to study the stability of the delayed financial model with pulse control,the related preliminary knowledge is introduced.Finally,by establishing the appropriate Lyapunov-Krasovskii function and using the inequality techniques a,the sufficient criteria for determining the stability of time-delayed financial system with impulsive control are obtained.