Research On Modified Function Projective Synchronization Of Fractional-order Complex Network With Unknown Parameters

With the rapid development of scientific complexity and the rapid development of network technology,the complex network of real life has more impact on the life of human society.The synchronization problem of complex dynamic network is gradually becoming the hotspot of research.It has been widely used in economic social,security communications,neural networks,traffic information,power systems,and many other aspects.Researchers in various industries have found that their respective fields need to be applied to the theory of complex networks.Therefore,the more in-depth research of complex networks required.At present,most of the researches on complex network synchronization are completely synchronous and some relatively simple synchronization methods,and the research direction of synchronization problems for complex networks is mainly to study how the dynamic behavior of each node is fully synchronized.However,since secure communication is a very difficult problem in today’s digital information age,improved function projection synchronization enables the drive system and the response network to be synchronized to a more complex scale function matrix,enabling secure communication by improving function projection synchronization to further increase the communication process The security of the information.In addition,the complex network described by the fractional order has stronger chaotic dynamical properties than the integer order,and can describe the complex network behavior in nature more specifically.This paper studies the improved function projection synchronizationproblem of fractional complex dynamic networks with unknown parameters.The main contents of this paper are as follows:In this paper,we study the modified function projective synchronization of fractional-order complex dynamical networks with unknown parameters.Firstly,on the basis of the fractional-order driving-response dynamic network,the controller is designed according to the fractional stability theorem,which makes the drive-response dynamic network realize the modified function projective synchronization with unknown parameters.Secondly,the paper studies the problem of time delay in the process of information transmission,so that we can make the drive-response dynamic network realize the modified function projective synchronization with unknown parameters and time delay.