Adaptive Estimation of Biological Rhythm in Crassulacean Acid Metabolism with Critical Manifold
Adaptive Estimation of Biological Rhythm in Crassulacean Acid Metabolism with Critical Manifold
复制标题
临界流形景天酸代谢生物节律的自适应估计
DOI：
10.1155/2013/856404
复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
and Haruo Suemitsu
中科院分区：
文献类型：
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作者：
Takami Matsuo;Yusuke Totoki;and Haruo Suemitsu
利用非线性理论模型研究了景天科酸代谢（CAM）植物内源光合作用昼夜振荡的机制。Blasius等人在整个连续时间中使用了充分反映CAM动态的微分方程。该模型显示了定期的内源性极限环振荡，在很宽的温度范围内是稳定的，符合实验数据的方式。在本文中，我们注意到CAM动力学的快模式的近似。利用慢流形的零-零近似，我们导出了由两个代数非线性方程定义的临界流形。临界流形允许我们给出液泡膜阶的代数估计。液泡膜有序度的动力学方程中包含了一个非线性函数，该非线性函数作为滞后开关给出了液泡膜脂质有序度的平衡值。我们识别的非线性函数的测量信号。利用非线性和临界流形的基函数展开，我们提出了一种自适应观测器来估计液泡膜阶数和非线性函数。
The mechanism of endogenous circadian photosynthesis oscillations of plants performing crassulacean acid metabolism (CAM) is investigated in terms of a nonlinear theoretical model. Blasius et al. used throughout continuous time differential equations which adequately reflect the CAM dynamics. The model shows regular endogenous limit cycle oscillations that are stable for a wide range of temperatures in a manner that complies well with experimental data. In this paper, we pay attention to the approximation of the fast modes of the CAM dynamics. Using the zero‐epsilon approximation of the slow manifold, we derive the critical manifold that is defined by two algebraic nonlinear equations. The critical manifold allows us to give the algebraic estimate of the order of the tonoplast membrane. The dynamic equation of the order of the tonoplast membrane includes the nonlinear function that gives the equilibrium value of the lipid order of tonoplast functions as a hysteresis switch. We identify the nonlinear function with the measurement signals. Using the basis function expansion of the nonlinear and the critical manifold, we propose an adaptive observer to estimate the tonoplast order and the nonlinear function.