Dynamic Behavior Analysis of DNA Subtraction Gate with Stochastic Disturbance and Time Delay

Abstract

AbstractAs one of the basic arithmetic gates of DNA circuits, the DNA subtraction gate plays an important role in the design and optimization of circuits. A nonlinear system with stochastic perturbations and delays is constructed to accurately describe the reaction process of DNA subtraction gates and comprehensively analyze the system dynamics. At the same time, enzyme recognition sites are added to the original basis of the DNA subtraction gate to increase the reaction rate. According to the law of conservation of quality, the dimensionality reduction of the system model with stochastic perturbation and time delay is performed, which greatly reduces the computational complexity. The properties of the solution of a DNA subtraction gate system are discussed, and the Lyapunov analysis proves that the model solution is global and unique. The properties of the solutions indicate that the constructed DNA subtraction gate system with stochastic perturbations and time delays is of practical significance. Through systematic ergodic analysis, it is found that the DNA subtraction gate system is distributed smoothly, which provides a theoretical basis for the realization of the DNA subtraction function. The results of numerical simulation show that the DNA subtraction gate can be implemented successfully under the influence of stochastic disturbance and time delay.KeywordsDNA subtraction gateTime delayStochastic perturbationStationary distributionErgodicity