Inverse Construction Of Discrete Chaotic Synchronization Systems And Research On Generalized Synchronization Methods

Chaos synchronization is an important aspect of chaos scientific research as well as an important part of chaotic secure communication.With the rapid development of digital logic circuits,the advantages of discrete synchronous module framework structure which is easy for hardware logic design are prominent,and the application of discrete chaotic synchronization method on some digital circuits becomes possible gradually,and the research of discrete chaotic synchronization method is of great significance.In this paper,starting from the dynamical behavior of discrete chaotic systems and focusing on the topic of generalized synchronization methods and inverse construction of discrete chaotic systems,this paper carries out a study on improved generalized synchronization methods for discrete chaotic systems,inverse construction methods for discrete chaotic synchronized systems and inverse construction methods based on discrete chaotic generalized synchronized systems.The main work of this paper is as follows:A general one-dimensional polynomial discrete chaotic mapping is constructed based on the "cycle three theorem",and more complex multi-stationary discrete chaotic systems and high-dimensional polynomial discrete chaotic systems with more complex dynamics are constructed based on the one-dimensional polynomial discrete chaotic mapping,to provide more types of driving or response systems for the subsequent research on discrete chaotic synchronous methods.To effectively improve the synchronization performance of discrete chaotic synchronization systems,this paper proposes a generalized synchronization method incorporating error coefficients and a generalized projection hybrid synchronization method.Such approaches can effectively accelerate the synchronization speed and reduce the synchronization error by controlling the error coefficient.To verify the effectiveness of these methods,the synchronization process between the driving system and the response system with different dimensions is analyzed in detail,and the simulation results show that these methods can effectively optimize synchronization performance.In the case of determining the discrete chaotic synchronization system first and verifying the synchronization performance later,the designed synchronization system would not ensure that the ideal synchronization state could be achieved.To solve this problem,this paper proposes an inverse construction method of discrete chaotic synchronous systems from a new perspective.This algorithm can not only optimize the synchronization performance of the discrete chaotic synchronous system but also build a discrete chaotic synchronous system with an ideal synchronous state of arbitrary dimensions which is valid for the drive-response synchronization method.To extend the application of the inverse construction method for chaotic synchronous systems,this paper proposes an inverse construction method for discrete chaotic generalized synchronous systems.The method combines the inverse construction with the generalized synchronization method incorporating error coefficients.The corresponding numerical simulation results show that this method can accelerate the synchronization speed,reduce the synchronization error,expand the synchronization region,and precisely control the dynamics of the synchronized system.Based on this method,a digital image encryption transmission system is designed to ensure the secure transmission of image information.The design of this system also provides a feasible solution for the application of discrete chaos synchronization theory in practical engineering.