Existence, Uniqueness, and Stability of Slowly Oscillating Periodic Solutions for Delay Differential Equations with Nonnegativity Constraints
Existence, Uniqueness, and Stability of Slowly Oscillating Periodic Solutions for Delay Differential Equations with Nonnegativity Constraints
复制标题
非负约束时滞微分方程慢振荡周期解的存在性、唯一性和稳定性
DOI：
10.1137/140980806
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Ruth J. Williams
中科院分区：
文献类型：
--
作者：
David Lipshutz;Ruth J. Williams
具有延迟反馈和非负性约束的确定性动力系统模型在科学和工程中有着广泛的应用。在某些条件下，观察到振荡行为，并且知道这种行为何时是周期性的是有意义的。本文考虑具有非负性约束的一维时滞微分方程作为这类模型的原型。当时滞间隔较长且动力学只依赖于当前和延迟状态时，得到了该类方程慢振荡周期解存在的充分条件。在进一步的假设下，包括可能更长的延迟间隔和限制动力学仅依赖于延迟状态，我们证明了这种解的唯一性和指数稳定性。为了证明这些结果，我们发展了一个理论来研究这些受限SOPS的微扰。我们用简单的生化反应网络模型和一个Internet模型来说明我们的结果。
Deterministic dynamical system models with delayed feedback and nonnegativity constraints arise in a variety of applications in science and engineering. Under certain conditions oscillatory behavior has been observed and it is of interest to know when this behavior is periodic. Here we consider one-dimensional delay differential equations with nonnegativity constraints as prototypes for such models. We obtain sufficient conditions for the existence of slowly oscillating periodic solutions (SOPS) of such equations when the delay/lag interval is long and the dynamics depend only on the current and delayed state. Under further assumptions, including possibly longer delay intervals and restricting the dynamics to depend only on the delayed state, we prove uniqueness and exponential stability for such solutions. To prove these results, we develop a theory for studying perturbations of these constrained SOPS. We illustrate our results with simple examples of biochemical reaction network models and an Internet r...
影响因子：
8.6
作者：
Mather W;Bennett MR;Hasty J;Tsimring LS
通讯作者：
Tsimring LS
影响因子：
3.4
作者：
Smolen, P;Baxter, DA;Byrne, JH
通讯作者：
Byrne, JH
DOI：
10.1073/pnas.0503858102
发表时间：
2005-10-11
影响因子：
11.1
作者：
Bratsun, D;Volfson, D;Hasty, J
通讯作者：
Hasty, J