Backstepping synchronization control for four-dimensional chaotic system based on DNA strand displacement

Backstepping control is an important nonlinear control design method, which realizes the control of complex systems by constructing control law step by step, and has significant advantages for dealing with complex nonlinear systems. This article proposes a synchronization technique for four-dimensional chaotic systems using a combination of backstepping control method and DNA strand displacement technology. By relying on theoretical knowledge of DNA molecules, five basic chemical reaction modules such as trigger reaction, reference reaction, catalytic reaction, annihilation reaction and degradation reaction are given to construct a four-dimensional DNA chaotic system. On the basis of the relevant theory of chaotic dynamics, the constructed system is analyzed by Lyapunov exponent diagram and spectral entropy complexity algorithm, and the results come to the conclusion that the system reveals extremely complex and varied dynamic behaviors. Combining DNA strand displacement technology with backstepping control method, four controllers are developed to ensure that the trajectories of two homogeneous chaotic systems are synchronized. The numerical simulation results validate the feasibility and applicability of the proposed method. The method proposed in this paper may provide some references in the field of DNA molecular chaos synchronization control.