Nonlinear Dynamics Estimation of CAM Plants Using Critical Manifold

Abstract

The mechanism of endogeneous circadian photosynthesis oscillations of plants performing crassulacean acid metabolism (CAM) is investigated in terms of a nonlinear theoretical model. In this report, we pay attention to the approximation of the fast modes of the CAM dynamics. Using the zero-epsilon approximation, we derive the critical manifold that is defined by two algebraic nonlinear equations. Using this critical manifold, we derive the algebraic estimates 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 fuzzy basis function expansion of the nonlinear and the critical manifold. we propose an adaptive observer to estimate the tonoplast order and the nonlinear function.