| In this thesis,the synchronization of two classes of Caputo fractional-order inertial-type neural networks is considered.The global Mittag-Leffler synchronization of fractional-order inertial-type neural networks with time delay and the asymptotic synchronization of delayed second-fractional-order fuzzy neural networks with impulsive effects are discussed by using the fractional-order inequality technique and Lyapunov function method.The thesis is divided into four chapters.The main contents are as follows:Chapter 1 is the introduction part.It begins by introducing the research context,goal,and significance of this thesis.Second,a brief overview of the research status of fractional-order neural networks,inertial neural networks and fractional-order inertial-type neural networks is provided.In Chapter 2,the global Mittag-Leffler synchronization of fractional-order inertial-type neural networks with time delay is discussed by designing two discontinuous control schemes with time delay and only one control input: one is state feedback control and the other is fractional-order adaptive control.Based on Lyapunov stability theory and fractional-order differential inequalities,some new sufficient criteria are given in the form of algebraic inequalities to ensure the global Mittag-Leffler synchronization of the studied systems.In Chapter 3,the global asymptotic synchronization of delayed second-fractional-order fuzzy neural networks with impulsive effects is discussed by designing two control schemes with fractional derivative terms.Based on the fractional-order Lyapunov functional method,several new sufficient criteria are given in the form of algebraic inequalities by using the nonreduced-order method and the impulsive fractional-order delay comparison principle to ensure the global asymptotic synchronization of the studied systems.Chapter 4 summarizes the work of the full text,and gives the work content that needs further research for subsequent research. |
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