Research On Synchronization Approaches Of Fractional-order Chaotic Systems With Time Delays

With the large-scale application of big data technologies such as cloud computing,social networking,and data mining,security issues such as information leakage are becoming increasingly prominent.As a supplement to the existing secure communication methods,chaotic secure communication is a new development direction of secure communication,which mainly solves the problem of low efficiency of the traditional encryption method encrypt high real-time video,image,and other large volumes of data encryption.It has the characteristics of low cost,real-time,and high security and can be integrated with the upper layer security mechanism to establish a new cross-layer security hierarchy.Chaotic secure communication will have broad application prospects in the field of secure communication.Fractional-order delayed chaotic systems have multiple positive Lyapunov exponents.The introduction of time-delay parameters into the chaotic system makes low-dimensional time-delay chaotic systems have higher dynamic complexity than non-time-delay hyperchaotic systems.These unique advantages are chaos confidentiality.The security of communication provides a theoretical guarantee.Therefore,fractional-order time-delay chaotic secure communication has important theoretical significance and practical application value in the field of secure communication.Chaos synchronization is the core problem to be solved in chaotic secure communication.This dissertation focuses on several types of fractional-order delayed chaotic systems synchronization and multi-switching dual combination synchronization application in secure communication,including combination synchronization,multi-switching combination synchronization,dual combination synchronization,multi-switching combination synchronization.Besides,a chaotic masking method is adopted to design a secure communication scheme based on the multi-switching dual combination synchronization of the fractional-order delayed chaotic system.This solution takes advantage of the synchronization correspondence between the system state vectors in the multi-switching dual combination synchronization,which is difficult to predict,information can flexibly select the driver to send,which improves flexibility and security of information transmission.The main contents can be summarized as follows:(1)The combination synchronization problem of fractional-order delayed chaotic system is discussed.First,the problem of combination synchronization is transformed into asymptotically stability problem of zero solution of fractional-order delayed error system,then,based on stability theory of linear fractional-order systems with multiple time delays,a sufficient condition for combination synchronization of three different fractional-order delayed chaotic systems is obtained.With the help of this theory and active control method,we design controllers to achieve combination synchronization of fractional-order delayed Financial system,fractional-order delayed Liu system and fractional-order delayed Lorenz system,numerical simulations have been performaed to demonstrate and verify the theoretical analysis.(2)The multi-switching combination synchronization of fractional-order time-delay chaotic systems is considered.The advantage of multi-switching mode is that it increases the error space of the synchronization systems,which makes it almost impossible for attackers to determine the synchronization combination of systems that may occur.It has great theoretical significance to generalize the problem of multi-switching combination synchronization to fractional-order delayed chaotic system because introducing time delay into fractional-order system enriches its dynamical characteristics,which has better unpredictability.Multi-switching combination synchronization is a generalization of combiantion synchronization,and combination synchrnization is a special case of multiswitching combination synchronization.Based on stability theory of linear fractionalorder systems with multiple time delays and active control method,we design controllers to achieve multi-switching combination synchronization of three different fractional-order delayed chaotic systems.The affect of the parameter value of feedback gain matrix on convergence rate of fractiona-order deleyed chaotic system is discussed.(3)The dual combination synchronization problem of fractional-order delayed chaotic systems is proposed.The dual synchronization model is a special case of chaotic synchronization.Its idea is derived from multiplexing chaos by synchronization.The dual combination synchronization is a generalization of the dual synchronization.The combined synchronization model has two driver systems and one response system.When the response system receives external interference,the system synchronization robustness is reduced.The dual combination synchronization combines the advantages of combination synchronization and combination-combination synchronization,increasing the number of drive systems and response systems.The problem of synchronization of fractional-order chaotic systems with time delays is in the primary stage,and there are lack of researches on the synchronization control of fractional-order delayed chaotic systems in many synchronization models.Based on the stability theory of linear fractional-order systems with multiple time delays,the controller is designed to realize dual combination synchronization of fractional-order delayed chaotic systems.Theoretical analysis and numerical simulation prove the effectiveness and correctness of the control method.(4)The multi-switching dual combination synchronization problem of fractional-order delayed chaotic systems is investigated.At present,there is no work on the synchronization of fractional-order delayed chaotic systems with dual combination synchronization and multi-switching mode.In this dissertation,the problem of multi-switching dual combination synchronization for four fractional-order delayed drive systems and two fractionalorder delayed response systems is studied.In multi-switching dual combination synchronization,the state variables of four drive systems synchronize with different state variables of two response systems simultaneously.Due to the complexity of dual combination synchronization and different synchronizations may be achieved for arbitrary pairs of state variables of drive and response systems,it will more secure and increase anti-attack ability to transmit information.(5)The application of multi-switching dual combination synchronizaiton to secure communication is discussed.The multi-switching dual combination synchronization is a generalized form of several types of synchronization models proposed in this paper.When the appropriate constant coefficient matrix values are set and the state variables of the drive system and response system are set to corresponding synchronization relationships,the multi-switching dual combination synchronization is degraded to other types of synchronization models in this dissertation,it is representative to study the application of this model in secure communications.Fractional-order delayed chaotic systems have multiple positive Lyapunov exponents,flexibility of information transmission methods,arbitrary setting of scale factor values between system state vectors,and multiple synchronization correspondences between state vectors.These advantages can increase system interpretation,difficulty and anti-attack ability,which greatly increase the security of communication system.