| Budget Amount *help |
¥3,140,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,300,000)
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| Research Abstract |
Biological rhythm is characterized by free-running, endogenous rhythms, ranging from periods of seconds(e. g. heart beat) to years(e. g. population dynamics). They can adjust themselves in a certain entrainment range to varying external influences, which thereby gives them greater plasticity for adaptation to changes in the environment than a rigid coupling could accomplish. Blasius et al.\cite{blasius2} investigated the mechanism of endogenous circadian photosynthesis oscillations of plants performing crassulacean acid metabolism(CAM) in terms of a nonlinear theoretical model. They used throughout continuous time differential equations which modes adequately reflect the CAM dynamics. By incorporating results from both a complementary and a continuous membrane model, a detailed description of the molecular malate transport in and out of the vacuole through the tonoplast membrane was achieved. Their analysis showed that the membrane effectively acts as a hysteresis switch regulating the
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oscillations. It thus provided a molecular basis for the circadigan clock. The model showed regular endogenous limit cycle oscillations that were stable for a wide range of temperatures, in a manner that complies well with experimental data. In this research, the nonlinear dynamical model of CAM is discussed from the control theoretical viewpoint. The state-variables of the nonlinear dynamic equations are an internal CO2 concentration, a malate concentration in the cytoplasm, a malate concentration in the vacuole, and an order of the tonoplast membrane. The input variables are an external CO2 concentration, a light intensity and a temperature. The output is assumed to be a part of the state variables. We can define the following problems in the control theoretical points of view. We presented a dynamic estimator of the tonoplast order and a fuzzy identifier of the nonlinear function in the dynamics of the tonoplast order. Next, we analyzed the CAM dynamics as a slow/fast system and the P-type feedback controller with the adaptive observer. Moreover, we proposed two types of the feedback controllers with a constant gain. The feedback controllers allow us to reshape the nullcline of the fast system of the CAM dynamics. The simulation results were given to examine the performance of the proposed dynamic estimator and controller using MATLAB/Simulnk. Finally, we proposed an instantaneous decay/growth rate that is a kind of generalized Lyapunov exponent and call the instantaneous Lyapunov exponent with respect to a decay function. The instantaneous Lyapunov exponent is one of the measures that estimate the decay and growth rates of flows of nonlinear systems by assigning a comparison function and can apply a stable system whose decay rate is slower than an exponential function. Less
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