Three-Variable Chaotic Oscillatory System Based on DNA Strand Displacement and Its Coupling Combination Synchronization

The synchronization control of two chaotic oscillatory systems is designed based on DNA strand displacement in the present work. Thus, combination synchronization of three 3-variable chaotic oscillatory systems is proposed based on DNA strand displacement. Firstly, five chemical reaction modules of double, displacement, adjustment, catalysis and degradation are designed. Based on these five modules, a 3-variable chaotic oscillatory system is designed. Secondly, based on the design principle of coupling terms and theory of stability, synchronization modules and coupling terms are added to three chaotic oscillatory systems to design combination synchronization of three 3-variable chaotic oscillatory systems based on DNA strand displacement. Modules and systems are implemented and tested using visual DSD and Matlab, and the simulation results are presented to demonstrate the effectiveness and correctness of the chemical reaction modules and systems. The combination synchronization of three 3-variable chaotic oscillatory systems is proposed based on DNA strand displacement, which may be extended to the reaction networks of DNA strand displacement and to the combination synchronization of multivariable chaotic oscillatory systems based on DNA strand displacement.