Backstepping Control of Projection Synchronization Among Two Three-Dimensional Heterogeneous Chaotic Systems Based on DNA Strand Displacement

Although many papers on synchronization of nonlinear systems have been published, relatively few studies have been done on projection synchronization in the DNA field. A backstepping control technology with DNA strand displacement is presented in this study, which achieves projection synchronization for two three-dimensional heterogeneous DNA chaotic systems. Some strand displacement reaction modules for designing DNA chaotic systems are given. By utilizing the related theory of DNA molecules and chaos theory, two heterogeneous DNA chaotic systems are presented, and their dynamic behaviors are analyzed to prove the correctness of the designed systems. Three controllers are obtained by using the combination of DNA strand displacement and backstepping control. Numerical simulation examples of two heterogeneous DNA chaotic systems illustrate that the controller has a better backstepping control effect and achieves the expected projection synchronization performance.