Adaptive Estimator for Biological Clock of Crassulacean Acid Metabolism

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 mode adequately reflect the CAM dynamics. They showed that the membrane effectively acts as a hysteresis switch regulating the oscillations. 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. The circadian period length is explained simply in terms of the filling time of the vacuole. In this paper, we discuss the nonlinear dynamical model of CAM from the control theoretical viewpoint. In particular, we present an adaptive observer to estimate the states and the nonlinear function in the dynamics of the tonoplast order assuming that the available signal is only the internal CO₂ concentration