亚洲免费av电影一区二区三区,日韩爱爱视频,51精品视频一区二区三区,91视频爱爱,日韩欧美在线播放视频,中文字幕少妇AV,亚洲电影中文字幕,久久久久亚洲av成人网址,久久综合视频网站,国产在线不卡免费播放

        ?

        Combination projection synchronization of fractional-order complex dynamic networks with time-varying delay couplings and disturbances

        2022-11-11 07:53:00JieFangDaWeiNanNanYinPeiZhaoYuandPengLiu
        Communications in Theoretical Physics 2022年11期

        Jie Fang,Da Wei,NanNan Yin,PeiZhao Yu and Peng Liu

        College of Electrical and information Engineering,Zhengzhou University of Light Industry,Zhengzhou,450002,China

        Abstract In this paper,the problem of combination projection synchronization of fractional-order complex dynamic networks with time-varying delay couplings and external interferences is studied.Firstly,the definition of combination projection synchronization of fractional-order complex dynamic networks is given,and the synchronization problem of the drive-response systems is transformed into the stability problem of the error system.In addition,time-varying delays and disturbances are taken into consideration to make the network synchronization more practical and universal.Then,based on Lyapunov stability theory and fractional inequality theory,the adaptive controller is formulated to make the drive and response systems synchronization by the scaling factors.The controller is easier to realize because there is no time-delay term in the controller.At last,the corresponding simulation examples demonstrate the effectiveness of the proposed scheme.

        Keywords:fractional-order complex networks,time-varying delay,combination projection synchronization,adaptive control

        1.Introduction

        In recent years,the rapid development of computer and information technology has brought mankind into the network age.A large number of complex systems existing in nature and human society can be described by various complex networks such as biological networks,information networks,transportation networks,and social networks.In recent decades,research on complex networks has penetrated into many different fields such as mathematics,life sciences,and social science.The scientific understanding of the quantitative and qualitative characteristics of complex networks has become an extremely important and challenging subject in scientific research today[1–4].Synchronization is a very common and important nonlinear phenomenon,which is widely used in secure communication,image encryption,bioscience,power systems,and other fields.The synchronization of complex networks is one of the most important research directions in the research of complex networks.So far,there have been reports of many complex network synchronization phenomena[5–13],such as complete synchronization,anti-synchronization,quasi-synchronization,global synchronization,outer synchronization,projection synchronization,function projective synchronization,combination synchronization and combination projection synchronization.

        The theory of fractional calculus is an extension of the theory of integer order calculus,and integer order calculus is only a special case of it.Fractional calculus can describe the physical phenomena in engineering applications more accurately than integer calculus and is more in line with engineering reality[14–19].Fractional-order complex networks exhibit more irregular and unpredictable dynamic behaviors than integer-order complex networks,and therefore exhibit broader development trends and application potentials.At present,more and more researchers are studying the synchronization of fractional complex networks.Reference[20]focused on the finite-time synchronization problem for fractional-order complex dynamical networks with intermittent control.Reference[21]studied the global exponential quasi-synchronization for fractional-order delayed dynamical networks via periodically intermittent pinning control.Reference[22]dealt with the finite-time synchronization problem between two different dimensional fractionalorder complex dynamical networks.Reference[23]realized the synchronization for a class of fractional-order linear complex networks via impulsive control.Reference[24]investigated the synchronization issue for a family of time-delayed fractionalorder complex dynamical networks with time delay,unknown bounded uncertainty and disturbance.Reference[10]presented an adaptive projective pinning control method for a fractionalorder complex network.Reference[25]proposed a complex projection synchronization with different coefficients in 1+Nnetworks.

        Combination synchronization refers to the generalized synchronization between multiple drive systems and multiple response systems[26–28].Combination synchronization increases the complexity of the synchronization system.When combination synchronization is applied to secure communication,the transmission signal can be divided and modulated to different drive systems,which improves the security and flexibility of secure communications.Projective synchronization is a special synchronization that reflects the proportional relationship between synchronization states by introducing a scaling factor,which can be regarded as an extension of full synchronization and anti-synchronization.Integrating of combine synchronization and projection synchronization can realize more complex synchronization and meet higher synchronization requirements.At present,the combination projection synchronization is mostly applied in synchronization between chaotic systems[29–33],and there are few studies on fractional-order complex networks.The research on combination projective synchronization of fractional-order complex networks can describe network synchronization more broadly in practical engineering applications.

        It is well known that there are always time delays in practical engineering applications.The time delay may destroy the dynamic characteristics and reduce the stability of the system,which is extremely detrimental to the control system[34–39].Time-varying delay coupling is a more general description of time delay,the constant time-delay coupling is its special case.The synchronization research of complex networks with time-varying delay coupling is more realistic and representative.Reference[40]investigated the synchronization problem for a class of fractional-order complex dynamical networks with and without time-varying delay.Reference[41]investigated adaptive pinning synchronization in fractional-order uncertain complex dynamical networks with delay.So far,there are relatively few studies on the synchronization of fractional-order complex networks with time-varying delays.

        Based on the above discussion,this paper studies the combination projection synchronization problem of multiple fractional-order complex dynamic networks with time-varying delay coupling and external interferences.First,some definitions,lemma,and assumptions are given to describe the combination projection synchronization of fractional-order complex dynamic networks.Second,based on the Lyapunov stability theory and fractional inequality theory,a nonlinear feedback controller and parameter adaptive laws are designed to make the drive-response system synchronize according to the corresponding scale factor matrix.There is no time-delay term in the controller,so it is easier to implement and apply.Finally,two simulation examples are carried out in this paper.The simulation results show that the controller in this paper can effectively overcome the influence of system time delay and disturbance,which has certain robustness.

        2.Model description

        The combination projection synchronization system consists of three drive systems and one response system.Three types of fractional-order complex dynamic networks with external interferences are described as the drive systems:

        the corresponding response system is:

        3.Controller design

        Choosing Lyapunov function as:

        Taking the derivative of the Lyapunov function,we can get:

        Because

        Then

        4.Numerical simulation

        The simulation results are shown in figure 4.It can still achieve combination projection synchronization when increasing the number of nodes and system dimensions of the complex networks,which further verifies the correctness of the theoretical analysis.

        5.Conclusion

        In this paper,the combination projection synchronization of fractional-order complex dynamic networks with time-varying delay couplings and disturbances is investigated.By using Lyapunov stability theory and fractional integral theory,the adaptive controller is designed to realize the combination projection synchronization among four fractional-order complex dynamic networks.The simulation examples show that the drive systems and response systems can be synchronized according to the scaling factors under the controller.The controller does not have a time-delay term,so it is easier to realize in engineering applications.This paper expands the number of synchronization systems and studies the combination projection synchronization between multiple fractional-order complex networks,which increases the complexity of the synchronization systems and provides a new idea for the application of fractional-order complex network synchronization in intelligent optimization,biomedical science and information science fields.In future studies,we will focus on addressing the following two problems:(1)How to realize the synchronization of fractional-order discrete systems?(2)How to solve the synchronization problem under input constraint?

        Acknowledgments

        The work was supported in part by the National Natural Science Foundation of China(Grant no.61775198,62076222,61903342),Henan Province Science and technology research project(Grant no.222102210059,222102210266,212102310455)

        Conflicts of interest

        The authors declare there is no conflict of interest regarding the publication of this paper.

        天堂无码人妻精品av一区| 中文字幕人乱码中文字幕乱码在线 | 色欲色香天天天综合网www| 中文字幕乱偷无码av先锋蜜桃| 欧美大香线蕉线伊人久久| 亚洲VR永久无码一区| av一区二区三区综合网站| 中文字幕在线观看| 午夜丰满少妇性开放视频| 国产真实乱XXXⅩ视频| 国产人妖伦理视频在线观看| 中文字幕精品一区二区精品| 日产无人区一线二线三线新版| 亚洲色AV天天天天天天| 一级一片内射视频网址| 一本精品99久久精品77| 一本色道久久99一综合| 日韩精品成人一区二区三区久久久| 亚洲国产中文字幕在线视频综合 | 九九精品国产99精品| 在线日本国产成人免费精品| 亚洲av无码久久精品色欲| 日本一区不卡在线| 国产精品丝袜一区二区三区在线 | 久久激情人妻中文字幕| 免费人成视频网站在线不卡| 大陆极品少妇内射aaaaaa| 亚洲VA不卡一区| 国产一区二区亚洲一区| 国产欧美精品一区二区三区四区| 少妇人妻在线视频| 成年女人18毛片毛片免费| 亚洲精品国产精品乱码视色| 国产亚洲精品aaaa片小说| 日本专区一区二区三区| 日韩av一区二区三区精品久久 | 日韩美女av一区二区| 欧洲美女黑人粗性暴交| 国产成人户外露出视频在线| 视频一区二区三区国产| 99久久99久久精品免费看蜜桃|