| The fractional-order differential dynamical systems with time delay is one of the important research problems in recent years.Due to different practical problems in biology and engineering science,many different fractional-order system models have been proposed.However,the research on the fractional differential dynamical system model with time delay is not perfect enough.In view of this,on the basis of previous work,in this thesis,several kinds of fractional-order differential dynamical systems with time delay are analyzed and studied.The details are as follows:1.The adaptive impulsive synchronization problem for a class of fractional-order chaotic systems with time delay is studied.Based on the existing model,according to the impulsive differential equations theory and the adaptive control theory,the adaptive impulsive controller and the parametric update law are designed,and the appropriate response system is constructed.Moreover,a new sufficient condition for adaptive impulsive synchronization of fractional-order chaotic systems with time delay is obtained.Finally,different initial conditions,fractional-order and time delay factors are considered,and the correctness of theoretical analysis is verified by numerical simulation of the system.2.The global synchronization problem of a class of fractional-order neural network models with time delay is studied.Based on the typical Caputo fractional-order neural network model with time delay,the time-varying term is introduced.By using Mittag-Leffler function and feedback control,the analytical formula of the synchronous controller is given,and the appropriate auxiliary function is constructed.Moreover,a sufficient condition for the synchronization of Caputo fractional-order neural network with time delay is obtained.Finally,different initial conditions,fractional-order and time delay factors are considered,and the numerical simulation of the system is carried out by MATLAB to verify the correctness of the theoretical analysis.3.The projective synchronization problem of a class of fractional-order neural network models with time delay is studied.Based on the second part of the research,different excitation functions are introduced.By designing a suitable controller,constructing the Lyapunov function,using fractional inequalities and the comparison principle of fractional-order differential equations with time delay,a sufficient conditionfor the projective synchronization of the Caputo fractional-order neural network with time delay are obtained.Finally,different initial conditions,fractional-order and time delay factors are considered,the correctness of the theoretical analysis is verified by numerical simulation of the system.4.The global synchronization problem of a class of new fractional-order neural networks with time delay is studied.Based on the research of the third part,the time-varying coefficient of the model is improved.Based on the new state feedback control,the analytical formula of the synchronous controller is given and the appropriate Lyapunov function is constructed.Moreover,some sufficient conditions for the global synchronization of the Caputo fractional-order neural networks with time delay are obtained.Finally,different initial conditions,fractional-order and time delay factors are considered,and the validity of the theory is verified by computer numerical simulation. |
