Nonlinear dynamics estimation of CAM plants using slow manifolds

Abstract

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 with the slow manifolds approximation.

Adaptive Estimation of Biological Rhythm in Crassulacean Acid Metabolism with Critical Manifold

“…Moreover, is not measurable because it is the order parameter of the membrane lipids. If is measurable, can be estimated using algebraic equation (11). The algebraic estimate of is obtained by…”

“…Finally, we design a first-order adaptive observer for online estimation of the nonlinear function in the dynamics of the tonoplast order using the output signal as the algebraic estimate of . The use of the algebraic estimate allows us to improve the convergence speed of the estimator in the previous paper [9,11,12]. The observer can attenuate the estimation error of the tonoplast order against the measurement noises.…”