Adaptive internal synchronization control of chaotic systems based on DNA strand displacement

Abstract

In the application of DNA‐based chaotic synchronization, the precise values of the system parameters are often complicated to attain due to the interference of external factors, thus weakening the performance of synchronization. In this paper, considering the case of unknown parameters in chaotic systems, a method of adaptive synchronization based on DNA strand displacement (DSD) is proposed. Firstly, the chain replacement reaction modules of emergence, activation and degradation are given through the design of DNA strand, which enable the realization of Yang chaotic system using the mass action dynamics law. Further, in order to achieve the estimation of the unknown parameters and the stability of the error system, the rules for identification of unknown parameters are derived and adaptive controllers are designed under the adaptive control principle. Finally, an internal synchronization approach is recommended to decompose the chaotic system into subsystems of different orders, which can freely choose subsystems to complete synchronization. Subsequently, numerical simulations show that DNA‐based adaptive controllers can fulfill the internal synchronization of Yang system with unknown parameters and are robust to parameter deviations. In addition, the strategy presented in this study can be extended to the synchronization control of other DSD‐based multivariable chaotic systems.