Synchronization of Hyper-Lorenz System Based on DNA Strand Displacement

Lorenz system is depicted by chemical reaction equations of an ideal formal chemical reaction network, and a series of reversible reactions are added into chemical reaction network in order to construct a cluster of hyper-Lorenz system. DNA as a universal substrate for chemical dynamics can approximate arbitrary dynamical characteristics of ideal formal chemical reaction network through auxiliary DNA strands and displacement reactions. Based on Lyapunov's stableness theory, a novel synchronization strategy is proposed. A 6-dimensional hyper-Lorenz system is taken as examples for simulation and shows that DNA strands displacement reactions can implement the synchronization of ideal formal chemical reaction networks. Numerical simulations indicate that synchronization based on DNA strand displacement is robust to the detection of DNA strand concentration, control of reaction rate, and noise.