Backstepping Synchronization Control for Three-Dimensional Chaotic Oscillatory System via DNA Strand Displacement

In previous work, a large number of articles have been published to implement coupled synchronization of chaotic systems in DNA-based reaction networks. Up to now, there have been few studies on backstepping synchronous control of chaotic systems through DNA strand displacement. A backstepping synchronization control approach for three-dimensional chaotic system by employing DNA strand displacement is developed in this study. First of all, using the programming properties of DNA molecules, four basic strand displacement reaction modules are given. In the light of these reaction modules as well as the law of mass action kinetics, a novel three-dimensional DNA chaotic system is presented. Second of all, by relying on backstepping control theory and DNA reaction modules, three synchronous controllers are developed to guarantee the synchronization between two three-dimensional DNA chaotic systems. Final of all, numerical simulation results are carried out to verify the validity and applicability of the backstepping synchronization control.