Mittag-Leffler And Quasi-uniform Synchronization Analysis Of Fractional-order Delayed Neural Networks

In recent years,fractional-order neural networks have been widely used in parallel computing,automatic control,optimization,and other fields.At the same time,a large number of research results on fractional-order neural network synchronization control have emerged.In this context,there are still many problems worthy of study in fractional-order neural networks that need further attention.Based on Lyapunov method,the synchronization problem of three kinds of fractional-order neural network models with time delay is studied in this paper.First,for the fractional-order inertial neural network system with delay defined by Caputo derivative,the system with inertia term under consideration is converted into two interconnected subsystems with fractional-order nonlinear coupling through appropriate variable substitution.Combining the delayed feedback controller,Lyapunov functional method and inequality analysis technique,a new algebraic criterion for global Mittag-Leffler synchronization of the system is obtained.Two numerical simulation examples verify the validity of the theoretical calculation results.Secondly,the fractional-order quaternion-valued neural network system with time delay and impulsive effects is established.Using the Banach contraction mapping principle,the existence results of solutions for fractional quaternion-valued neural networks are obtained.The hybrid control strategy is to overcome the difficulties caused by delay factors,impulses and fractional derivative operators in the process of achieving global Mittag-Leffler projection synchronization of the system,and the flexibility of searching the control gain constant is also greatly improved under synchronization conditions.In order to verify the effectiveness of the hybrid control strategy,two numerical simulation examples are given,and the data value is extended from real number to quaternion.Finally,the quasi-uniform synchronization problem of fractional fuzzy neural networks with proportional and distributed delays is studied.Fully considering the influence of the order of the Caputo derivative,the network system coefficient and the control gain constant on the synchronization behavior,using various inequality techniques to establish two algebraic criteria for quasi-uniform synchronization under the derivative order interval(0,1)and(1,2).The results obtained are related to the control gain coefficient and the order of the derivative.In order to verify the feasibility and practicability of the theoretical results,Matlab is used for numerical simulation.