一类具有超昼夜糖皮质激素节律的急性应激模型解的存在性和稳定性分析
Existence and stability analysis of solutions for a ultradian glucocorticoid rhythmicity and acute stress model
摘要：
下丘脑-垂体-肾上腺（HPA）轴对身体和精神的挑战做出反应，部分通过控制身体的皮质醇水平来维持体内平衡。HPA轴的失调与许多应激相关疾病有关。对于HPA轴的结构化模型，其中包括糖皮质激素受体，但不考虑系统的响应延迟，我们分析了线性和非线性稳定性的固定解决方案。第二个数学模型，描述了HPA轴的自我调节活动的机制，并考虑到系统响应的延迟，我们证明了周期解的存在性，在一定的假设范围内的参数值和分析这些解决方案的稳定性相对于时间延迟值。
英文摘要：
The hypothalamic pituitary adrenal (HPA) axis responds to physical and mental challenge to maintain homeostasis in part by controlling the body's cortisol level. Dysregulation of the HPA axis is implicated in numerous stress-related diseases. For a structured model of the HPA axis that includes the glucocorticoid receptor but does not take into account the system response delay, we analyze linear and non-linear stability of stationary solutions. For a second mathematical model that describes the mechanism of the HPA axis self-regulatory activities and takes into account a delay of system response, we prove existence of periodic solutions under certain assumptions on ranges of parameter values and analyze stability of these solutions with respect to the time delay value.
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