Sufficient and necessary conditions for global stability of genetic regulator networks with time delays

This paper is concerned with the global stability of the nonlinear model for genetic regulator networks (GRNs) with time delays. Four new sufficient and necessary conditions for global asymptotic stability and global exponential stability of the equilibrium point of GRNs are derived. Specifically, using comparing theorem and Dini derivation method, three weak sufficient conditions for global stability of GRNs with constant time delays are proposed. Finally, a general GRN model is used to illustrate the effectiveness of the proposed theoretical results. Compared with the previous results, some sufficient and necessary conditions for Lyapunov stability of GRNs are proposed, which are not seen before.创新点本文讨论了一类非线性时滞基因调控网络的全局稳定性,给出了四个关于基因调控网络平衡点全局渐近稳定和全局指数稳定的充分必要条件。此外,本文通过运用比较定理和Dini导数,提出了三个关于基因调控网络全局稳定的充分条件。最后,通过一个典型的基因调控网络模型,进一步验证了本文给出结论的有效性。与已有基因调控网络稳定性的结论相比,基于Lyapunov稳定性的充分必要条件在以前的文献中未见到。