Abstract
AbstractDNA molecular technology has gradually matured and has been widely used in the design of nanomaterials and chemical oscillators. In order to ensure the correct setting of DNA molecular oscillator, it is necessary to thoroughly study the dynamic behavior of system. This paper studies the dynamics system of DNA molecular oscillator based on DNA strand displacement. Modeling the reaction process transforms the reaction process into a specific mathematical model. The research results show that the influence of time delay is not considered in an ideal state. Stability near the equilibrium point of system is determined by initial reaction substrate concentration and reaction rate. Considering the time delay of separation of DNA double-stranded molecules in the reaction process, the time delay parameter is added to the system model. As the time delay increases, the system changes from a stable state to an unstable state and Hopf bifurcation occurs. At the same time, the study found that both Hopf bifurcation direction and the periodic solution are closely related to the time delay parameter. The result of numerical simulation proves the correctness of our conclusion.KeywordsDNA molecular oscillatorTime delayDNA strand displacementHopf bifurcationHopf bifurcation direction
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