Synchronization Control Of Fractional-order Fuzzy Cellular Neural Networks With Delays

The dynamic research of fractional-order fuzzy cellular neural networks(FCNNs)has been widely focused on because of their extended applications in image processing,associative memory,and pattern recognition,and these applications largely depend on the dynamic behaviors of systems.Recently,another scholar proposed a class of fractionalorder FCNNs with interactions and investigated the criteria for its realization of global asymptotic synchronization.This model has important practical significance and research value due to interactions between two networks being inevitable in reality.However,there are few references that have analysis it.Considering the importance of global MittagLeffler synchronization and fixed-time synchronization to the study of system dynamics,and the interference of time delay on the dynamic behavior of the system,based on the above neural network model,this thesis aims to explore the conditions for achieving global Mittag-Leffler synchronization and fixed-time synchronization with the addition of time delay.The specific research work is as follows:First,the global Mittag-Leffler synchronization of fractional-order FCNNs with delays and interactions is investigated.Under the assumptions of Lipschitz continuity of activation functions and interaction functions,sufficient conditions are acquired to reach the global Mittag-Leffler synchronization of the discussed systems under feedback control and adaptive control individually.Besides,the sufficient conditions for the system to realize global Mittag-Leffler synchronization are considered when the interaction functions of the system is bounded.Then,the fixed-time synchronization of fractional-order FCNNs with delays and interactions is also investigated.On the ground of an enhanced fixed-time stability theorem,under the assumptions of Lipschitz continuity of activation functions and interaction functions and the boundedness of interaction functions,several adequate conditions are obtained to vouch for the fixed-time synchronization of the discussed systems through two categories of control schemes.Moreover,in terms of another fixed-time stability theorem,the different upper-bounding estimating formulas for settling time are given,and the distinctions between them are pointed out.Finally,based on a method to find the numerical solution of fractional-order differential equations,numerical examples of a two-dimension system and a three-dimension system are delivered at length to demonstrate the acquired conclusions.