论文标题
泰森·洪·诺沃克昼夜节律振荡器模型的动力学
Dynamics of the Tyson-Hong-Thron-Novak circadian oscillator model
论文作者
论文摘要
我们研究了泰森，洪，托隆和诺瓦克提出的昼夜节律振荡器模型的动力学。该模型表明果蝇中昼夜节律的分子机制。在对平衡的详细研究后，我们进一步研究了mRNA降解和合成速率的影响。当mRNA降解速率相当快时，我们证明该模型中没有周期性轨道。当mRNA降解速率足够缓慢时，该模型将转换为缓慢的系统。然后，基于几何奇异扰动理论，我们证明了塔纳德爆炸，松弛振荡，同骨/杂斜轨道和鞍节点分叉的存在，这是mRNA降解和合成变化的速率。最后，我们给出了获得的结果的生物学解释，并指出该模型可以转化为liénard样方程，这可能有助于研究一般情况的动力学。
We study the dynamics of a circadian oscillator model which was proposed by Tyson, Hong, Thron and Novak. This model indicates a molecular mechanism for the circadian rhythm in Drosophila. After giving a detailed study of the equilibria, we further investigate the effects of the rates of mRNA degradation and synthesis. When the rate of mRNA degradation is rather fast, we prove that there are no periodic orbits in this model. When the rate of mRNA degradation is slow enough, this model is transformed into a slow-fast system. Then based on the geometric singular perturbation theory, we prove the existence of canard explosion, relaxation oscillations, homoclinic/heteroclinic orbits and saddle-node bifurcations as the rates of mRNA degradation and synthesis change. Finally, we give the biological interpretation of the obtained results and point out that this model can be transformed into a Liénard-like equation, which could be helpful to investigate the dynamics of the general case.
