Asymptotic stability criteria for genetic regulatory networks with time-varying delays and reaction-diffusion terms
Asymptotic stability criteria for genetic regulatory networks with time-varying delays and reaction-diffusion terms
复制标题
具有时变延迟和反应扩散项的遗传调控网络的渐近稳定性准则
DOI：
10.1007/s00034-015-0006-8
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Yantao Wang
中科院分区：
文献类型：
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作者：
Yuanyuan Han;Xian Zhang;Yantao Wang
研究了具有反应扩散项的时滞遗传调控网络在Dirichlet边界条件和Neumann边界条件下的渐近稳定性问题。首先，通过构造一个新的Lyapunov-Krasovskii泛函，利用Jensen不等式、Wirtinger不等式、Green第二恒等式和互凸方法，建立了不需要限制时滞导数上界小于1的时滞相关渐近稳定性判据。因此，我们建立的稳定性判据比现有判据更保守，扩大了理论结果的应用范围。此外，还证明了在Dirichlet边界条件下得到的判据保留了反应扩散项的信息，而在Neumann边界条件下得到的判据则不存在这些信息。从理论上证明了本文所建立的稳定性判据比已有的稳定性判据保守性更小。最后，通过数值算例验证了理论结果的有效性。
This paper investigates the asymptotic stability problem for delayed genetic regulatory networks with reaction–diffusion terms under both Dirichlet boundary conditions and Neumann boundary conditions. First, by constructing a new Lyapunov–Krasovskii functional and using Jensen’s inequality, Wirtinger’s inequality, Green’s second identity and the reciprocally convex approach, we establish delay-dependent asymptotic stability criteria that do not require a restriction of the upper bounds of the delays’ derivatives being less than 1. Thus, the stability criteria that we establish are less conservative than the existing criteria and extend the range of applications of the theoretical results. In addition, it is shown that the obtained criterion under Dirichlet boundary conditions retains the information about the reaction–diffusion terms, while these do not exist in the criterion under Neumann boundary conditions. It is then theoretically presented that the stability criteria established in this paper are less conservative than the existing ones. Finally, numerical examples are given to illustrate the effectiveness of the theoretical results.