IEEE Trans Nanobioscience. 2022 Jan;21(1):55-64. doi: 10.1109/TNB.2021.3111109. Epub 2021 Dec 30.
In this paper, we focus on the cluster synchronization of reaction-diffusion genetic regulatory networks (RDGRNs) with time-varying delays, where the state of the system is not only time-dependent but also spatially-dependent due to the presence of the reaction-diffusion terms. First, we construct an intermittent space-dividing controller that effectively combines the two control strategies, making it more cost-effective. Furthermore, based on the activation function division approach, we propose a regulation function division method that can improve the delay upper bound of RDGRNs; meanwhile, the cluster synchronization criteria of RDGRNs under the proposed controller are derived based on the Lyapunov theory and Halanay's et al. inequality techniques. Finally, the criteria's effectiveness is demonstrated by numerical examples of the system in one- and two-dimensional space.
在本文中，我们关注时变时滞反应扩散遗传调控网络（RDGRNs）的簇同步问题，其中系统的状态不仅取决于时间，还取决于由于反应扩散项的存在而导致的空间依赖性。首先，我们构建了一种间歇空间分割控制器，有效地结合了两种控制策略，从而降低了成本。此外，基于激活函数划分方法，我们提出了一种调节函数划分方法，可以提高 RDGRNs 的延迟上界；同时，基于李雅普诺夫理论和 Halanay 等人的不等式技术，推导出了在所提出的控制器下 RDGRNs 的簇同步准则。最后，通过对一维和二维空间系统的数值示例验证了该准则的有效性。
