双基因网络的动态特性
Dynamical Properties of a Two-gene Network with Hysteresis
AI总结：
研究双基因调控网络的动态特性，采用混合系统模型分析其连续/离散动态和滞后特性，揭示参数范围内极限环的存在及其稳定性。
摘要：
本文推导了一个双基因调控网络的数学模型，并分析了其若干性质。由于存在混合连续/离散动态和滞后现象，我们采用混合系统模型来捕捉系统的动态。所提出的模型结合了二进制滞后特性，具有不同的阈值，以捕捉基因间的相互作用。我们分析了系统解的性质以及平衡点的渐近稳定性，作为参数函数。我们的分析揭示了在某些参数范围内存在极限环，这种行为与滞后有关。极限环定义点集被刻画，并研究其渐近稳定性特性。此外，极限环的稳定性对小扰动具有鲁棒性。数值模拟用于说明结果。
英文摘要：
A mathematical model for a two-gene regulatory network is derived and several of their properties analyzed. Due to the presence of mixed continuous/discrete dynamics and hysteresis, we employ a hybrid systems model to capture the dynamics of the system. The proposed model incorporates binary hysteresis with different thresholds capturing the interaction between the genes. We analyze properties of the solutions and asymptotic stability of equilibria in the system as a function of its parameters. Our analysis reveals the presence of limit cycles for a certain range of parameters, behavior that is associated with hysteresis. The set of points defining the limit cycle is characterized and its asymptotic stability properties are studied. Furthermore, the stability property of the limit cycle is robust to small perturbations. Numerical simulations are presented to illustrate the results.
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