The mechanism o f endogenous circadian photosynthesis oscillations of plants perjorming 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 reJect the CAM dynamics. They showed that the membrane effectively acts as a hysteresis switch regulating the oscillations. 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 COz concentration. We adopt a nonlinear error function in the error feedback term.

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.

Neurons of primary sensory cortices are known to have specific responsiveness to elemental features. To express more complex sensory attributes that are embedded in objects or events, the brain must integrate them. This is referred to as feature binding and is reflected in correlated neuronal activity. We investigated how local intracortical circuitry modulates ongoing-spontaneous neuronal activity, which would have a great impact on the processing of subsequent combinatorial input, namely, on the correlating (binding) of relevant features. We simulated a functional, minimal neural network model of primary visual cortex, in which lateral excitatory connections were made in a diffusive manner between cell assemblies that function as orientation columns. A pair of bars oriented at specific angles, expressing a visual corner, was applied to the network. The local intracortical circuitry contributed not only to inducing correlated neuronal activation and thus to binding the paired features but also to making membrane potentials oscillate at firing-subthreshold during an ongoing-spontaneous time period. This led to accelerating the reaction speed of principal cells to the input. If the lateral excitatory connections were selectively (instead of "diffusively") made, hyperpolarization in ongoing membrane potential occurred and thus the reaction speed was decelerated. We suggest that the local intracortical circuitry with diffusive connections between cell assemblies might endow the network with an ongoing subthreshold neuronal state, by which it can send the information about combinations of elemental features rapidly to higher cortical stages for their full and precise analyses.

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.

The Lyapunov exponent gives a measure of the mean decay/growth rates of the flows of nonlinear systems. However, the Lyapunov exponent needs an infinite time interval of flows and the Jacobian matrix of system dynamics. In this paper, we propose an instantaneous decay/growth rate that is a kind of generalized Lyapunov exponent and call the instantaneous Lyapunov exponent (ILE) 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. Moreover, we propose a synchronization measure of two signals using the ILE.