| DNA strand displacement technique has attracted widespread attention from scholars both domestically and abroad due to its highly parallel computing capabilities,strong storage capacity,and strong programmability.With the rapid development of DNA computing,researchers have delved into applying DNA strand displacement technology to the field of chaos control.Currently,a considerable amount of research has been done on the construction and synchronization control of chaotic systems based on DNA strand displacement.However,most of the constructed DNA chaotic systems are three-dimensional,and the methods used to achieve synchronization control are based on coupling control,resulting in relatively simple dynamic behavior and synchronization control methods.To enrich the theoretical research of DNA chaotic systems,this article combines the backstepping control method with DNA strand displacement technology to achieve backstepping synchronization control of two threedimensional DNA chaotic systems,projection synchronization of two three-dimensional DNA heterogeneous chaotic systems,and backstepping projection synchronization of two fourdimensional DNA chaotic systems,which are applied to the field of secure communication.The main contents of this paper are as follows:A synchronization control scheme combining DNA strand displacement reaction module with backstepping control technique is proposed to address the issue of limited chaos synchronization control methods for DNA strand displacement and relatively simple controller design.Different DNA reaction modules are designed,and a three-dimensional DNA chaotic system is constructed based on the theory of mass action kinetics.Three backstepping controllers are designed in combination with the backstepping control technology,and the backstepping synchronization of two three-dimensional DNA chaotic systems is achieved.Compared with previous control technologies,this technology has a more complex design process,and each step of the controller design is based on the Lyapunov stability theory,making the designed controller more stable in performance.Chaotic synchronization types for DNA strand displacement are mainly focused on the research problems of coupling synchronization and combination synchronization.A backstepping control technique based on DNA strand displacement is proposed to achieve projection synchronization between two three-dimensional heterogeneous DNA chaotic systems.Two DNA chaotic systems with different structures are established using the basic reaction module of DNA strand displacement,and the relevant theories of chaotic dynamics are used to analyze and verify their dynamic behaviors.By combining the backstepping control technique,projection synchronization between the two DNA chaotic systems is achieved,and the selection of the synchronization scaling factor has greater flexibility,which can improve the security performance of confidential communication.The construction of DNA strand displacement chaotic systems mainly focuses on the research of three-dimensional chaotic systems and their synchronization control applications.A backstepping synchronization control technique based on four-dimensional DNA strand displacement chaotic systems and its application in the field of secure communication are proposed.By using DNA reaction modules and the theory of mass action kinetics,the dimension of the three-dimensional DNA chaotic system is extended to four dimensions,and the complex dynamic behavior is analyzed and verified using Lyapunov exponents and bifurcation diagrams.Combined with the backstepping control technique,a backstepping controller is gradually designed based on the Lyapunov stability theory,and the backstepping projection synchronization of two four-dimensional DNA chaotic systems is achieved.On this basis,four different encryption signals are constructed.A secure communication scheme is proposed,which realizes the encryption and decryption functions of backstepping projection synchronization of four-dimensional DNA chaotic systems.This provides a theoretical basis and reference for the synchronization control and secure communication applications of DNA chaotic systems.This article extensively discusses the synchronization problem of DNA chaotic systems,focusing on two aspects: the construction of DNA chaotic systems and the backstepping synchronization control technology.Furthermore,it explores the application of DNA chaos synchronization in the field of secure communication.The reliability and rationality of the proposed method are validated through numerical simulation results. |
