Abstract
The realization of molecular logic circuit is inseparable from the design and analysis of catalytic reaction chain, and the DNA catalytic gate plays an important role in it. Discuss the nature of the solution to DNA catalytic reaction system, using Khasminskii's periodicity and Lyapunov analysis methods to obtain the existence of non-trivial positive periodic solutions of the system, and the solution is globally attractive. The existence of the solution indicates that according to the mathematical model established by the DNA catalytic reaction system, the system may reach the expected concentration value of an ideal state and obtain better reaction data, which provides a theoretical basis for the realization of the DNA catalytic gate function. Numerical simulation results show that under the influence of random disturbance and periodic parameters, the solution to the random DNA catalytic reaction system exists and is globally attractive, which also reflects that the DNA catalytic reaction system can reach an ideal reaction state. The solution to the DNA catalytic system with random disturbance will converge on a certain value and oscillate periodically between the solution to the deterministic system.
Highlights
At present, it has been proved that nucleic acid is a multifunctional construction material for engineering molecular structures and devices
The DNA catalytic reaction system is analyzed for solution, and it is assumed that the reaction material is added regularly to keep the reaction continuing
Considering that the reaction will be affected by random interference, here is mainly white noise, so adding random interference to the DNA catalytic system is more in line with the actual reaction of the system
Summary
It has been proved that nucleic acid is a multifunctional construction material for engineering molecular structures and devices. Most of the research results are about the realization of logical operations and arithmetic operations in DNA circuits, and few involve the dynamics of the reaction system In this case, this article mainly constructs a nonlinear mathematical model for the DNA catalytic gate reaction processes to simplify certain steps of the DNA catalytic reaction, random interference factors are considered, and the reaction process is analyzed from the perspective of kinetics. In this paper, based on the DNA catalytic gate reaction process, and taking into account the influence of random disturbance factors, a stochastic differential system is established. The Lyapunov analysis method is used to prove that the system has a nontrivial positive periodic solution, which verifies that the random DNA catalytic gate system model with periodic function constructed in this paper is in accordance with practical significance. The results of numerical simulation verify the conclusions of this paper
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