Yusuke Totoki

Firing Pattern Estimation of Synaptically Coupled Hindmarsh-Rose Neurons by Adaptive Observer

In this paper, we present adaptive observers for synaptically coupled Hindmarsh-Rose(HR) neurons with the membrane potential measurement under the assumption that some of parameters in an individual HR neuron are known. Using the adaptive observers for a single HR neuron, we propose a two-stage merging procedure to identify the firing pattern of a model of synaptically coupled HR neurons. The procedure allows us to recover the internal states and to distinguish the firing patterns of the synaptically coupled HR neurons, with early-time dynamic behaviors.

Firing Pattern Estimation of Biological Neuron Models by Adaptive Observer

In this paper, we present three adaptive observers with the membrane potential measurement under the assumption that some of parameters in HR neuron are known. Using the Strictly Positive Realness and Yus stability criterion, we can show the asymptotic stability of the error systems. The estimators allow us to recover the internal states and to distinguish the firing patterns with early-time dynamic behaviors.

Adaptive Observer for Biological Clock of Crassulacean Acid Metabolism with Partial States

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. 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. We adopt a nonlinear error function in the error feedback term.

Nonlinear dynamics estimation of CAM plants using slow manifolds

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

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.

Local intracortical circuitry not only for feature binding but also for rapid neuronal responses

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.

Parameter and input estimation in Hindmarsh-Rose neuron by adaptive observer

In this paper, we present adaptive observers of Hindmarsh-Rose (HR) neurons with the membrane potential measurement under the assumption that all parameters in an individual HR neuron are unknown. Using the time-varying adaptive observer for MIMO systems, we propose two adaptive observers to identify the firing pattern of a model of synaptically coupled HR neurons. The procedure allows us to recover the internal states and to distinguish the firing patterns of the synaptically coupled HR neurons, with early-time dynamic behaviors.

Decay/growth rate evaluation by Malthusian parameter estimation and its application to ECG signals

The dynamics of cardiovascular rhythms have been widely studied due to the key aspects of the heart in the physiology of living beings. Cardiac rhythms can be either periodic or chaotic. The Lyapunov exponent has been used as a measure of chaos in time series data from cardiovascular rhythms. The Malthusian parameter is closely related with the Lyapunov exponent. In this paper, we propose the adaptive observers to estimate the time-varying the Malthusian parameter as the decay and growth rate using the gradient method. We apply the estimators to evaluate the decay and growth rate of pathological cardiovascular rhythms and compare the obtained results with the instantaneous Lyapunov exponent and the recurrence plot.

DECAY/GROWTH RATE ESTIMATION USING INSTANTANEOUS LYAPUNOV EXPONENT

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.

Control of biological clock in crassulacean acid metabolism using nullcline design

The nonlinear dynamical behavior of the crassulacean acid metabolism 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. We have recently presented a dynamic estimator of the tonoplast order and a fuzzy identifier of the nonlinear function in the dynamics of the tonoplast order. In this paper, we propose two types of the feedback controllers of the CAM model using the external CO2 concentration and the light intensity as an input.