| After Lorenz found the chaotic attractor in the weather forecast system and proposed the famous "Butterfly Effect",chaos has been a hot topic in the field of nonlinear research.Chaotic system is a kind of complex nonlinear dynamic system,and its research is gradually extended from real chaotic system to complex chaotic system.Chaos theory has been widely used,involving many fields such as economy,finance,biology,physics,chemical industry,aerospace and so on.Because of the inherent randomness and disorder of complex chaos system,it is especially suitable for the carrier of secure communication.Complex variables have real and imaginary parts,which can increase the amount of information transmitted by the system and greatly improve the security of information transmission.The research of complex dynamics system is just beginning,and there are many deficiencies in the related research,such as the time delay factors and external disturbances.Therefore,combining the stability theorem of nonlinear systems and the related properties of complex chaotic systems,this paper makes further analysis and basic research on the qualitative theory and synchronization control of complex chaotic systems with time delay:(1)Characteristic analysis and self time-delay synchronization of complex Chen chaotic systems with time delayBased on the complex Chen chaos system,a complex Chen chaos system with time delay is constructed,and the influence of time delay on the complex chaos is studied.The dynamic characteristics of the complex Chen chaotic system with time delay are studied by Lyapunov index,Pangalay cross section,phase diagram and bifurcation graph.Compared with the original system,the dynamic properties of the complex chaotic system with time delay are more abundant,the volume of attractors in phase space is larger,and more complex and random sequences can be generated.Finally,the self time-delay synchronization of the complex Chen chaos system is proposed.The synchronization controller is designed,and the mathematical and numerical simulation are carried out to verify the effectiveness of the controller.(2)Complex modified projective synchronization of time-delay complex chaotic systemBased on the time-delay complex Chen chaotic system,its complex modified proportional projection synchronization(CMPS)is studied.First,the definition of the time-delay complex chaotic system is given,and then the synchronous controller is designed according to the principle of feedback control.Finally,the effectiveness of the controller is proved through mathematical proof and numerical simulation.(3)Secure communication scheme for wireless body area network based on CMPSBased on the CMPS of the time-delay complex Chen system,the application of secure communication in wireless body area networks is studied.First,the concept and communication model of wireless body area network are introduced.Sensors installed on various parts of the body collect the user's physiological information,and after the user terminal completes the information encryption,it is sent to the remote terminal for decryption.Its encryption and decryption are suitable for the use of time-lag complex chaotic systems.Synchronize to solve.Then proposed a secure communication scheme based on.Finally,the performance indicators of the program are analyzed.The communication scheme has the advantages of simple structure,zero error rate,fast transmission,and high security.(4)Design of simulation software for complex chaotic systemBased on the graphical operation interface,a complex chaos system simulation software was designed by using the complex chaos related simulation programs accumulated in the past.With this software,the various parameters of the system can be adjusted arbitrarily,and the attractor,phase diagram and Poincaré cross section of complex chaos can be seen intuitively and vividly.Through this software,you can further study and study the characteristics and application prospects of complex chaotic systems. |
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