Stability Analysis and Hopf Bifurcation Research for DNA Strand Displacement with Time delay

被引：1

作者：

Liu, Yanhong ^{[1
]}

Lv, Hui ^{[1
]}

Zhou, Changjun ^{[1
]}

Yin, Zhixiang ^{[2
]}

Fang, Xianwen ^{[2
]}

Zheng, Zhonglong ^{[3
]}

Zhang, Qiang ^{[1
,4
]}

机构：

[1] Dalian Univ, Minist Educ, Key Lab Adv Design & Intelligent Comp, Dalian, Peoples R China

[2] Anhui Univ Sci & Technol, Sch Math & Big Data, Huaian, Peoples R China

[3] Zhejiang Normal Univ, Coll Math Phys & Informat Engn, Jinhua, Peoples R China

[4] Dalian Univ Technol, Dept Comp Sci & Technol, Dalian, Peoples R China

来源：

2018 IEEE SMARTWORLD, UBIQUITOUS INTELLIGENCE & COMPUTING, ADVANCED & TRUSTED COMPUTING, SCALABLE COMPUTING & COMMUNICATIONS, CLOUD & BIG DATA COMPUTING, INTERNET OF PEOPLE AND SMART CITY INNOVATION (SMARTWORLD/SCALCOM/UIC/ATC/CBDCOM/IOP/SCI) | 2018年

基金：

中国国家自然科学基金;

关键词：

time delay; nonlinear dynamic system; DNA strand displacement; local stability; Hopf bifurcation; PLATFORM; MODEL;

D O I：

10.1109/SmartWorld.2018.00074

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper, a nonlinear system with time delay mode for DNA strand displacement based on toehold exchange firstly is proposed. The boundedness of all the state variables of the DNA strand displacement system is proved. After that, local stability analysis is performed around the positive equilibrium point to obtain a necessary and sufficient condition for local stability, which depend on the coefficients of the characteristic equation corresponding to linearization of the system. In addition, the existence of the Hopf bifurcation is analyzed, which shows that the time delay parameter will guarantee that the system is stable within a certain range. However, Hopf bifurcation and chaos occur when the time delay parameter increases continuously and even exceeds the critical value. At last, numerical simulations have verified the correctness and validity of the DNA strand displacement studies.

引用

页码：228 / 233

页数：6

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