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136
Modeling a simple choice task: stochastic dynamics of mutually inhibitory neural groups
 Stochastics & Dynamics
, 2001
"... We describe the dynamical and bifurcational behavior of two mutually inhibitory, leaky, neural units subject to external stimulus, random noise, and ‘priming biases. ’ The model describes a simple forced choice experiment and accounts for varying levels of expectation and control. By projecting the ..."
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Cited by 32 (17 self)
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We describe the dynamical and bifurcational behavior of two mutually inhibitory, leaky, neural units subject to external stimulus, random noise, and ‘priming biases. ’ The model describes a simple forced choice experiment and accounts for varying levels of expectation and control. By projecting the model’s dynamics onto slow manifolds, using judicious linear approximations, and solving for onedimensional (reduced) probability densities, analytical estimates are developed for reaction time distributions and shown to compare satisfactorily with ‘full ’ numerical data. A sensitivity analysis is performed and the effects of parameters assessed. The predictions are also compared with behavioral data. These results may help correlate lowdimensional models of stochastic neural networks with cognitive test data, and hence assist in parameter choices and model building. 1 Introduction and
Fast switches in relay feedback systems
 AUTOMATICA 35 (1999) 539—552
, 1999
"... Relays are common in automatic control systems. Even linear systems with relay feedback are, however, far from fully understood. New results are given about the behavior of these systems via a statespace approach. It is proved that there exist multiple fast switches if and only if the sign of the ..."
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Cited by 29 (6 self)
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Relays are common in automatic control systems. Even linear systems with relay feedback are, however, far from fully understood. New results are given about the behavior of these systems via a statespace approach. It is proved that there exist multiple fast switches if and only if the sign of the first nonvanishing Markov parameter of the linear system is positive. Fast switches are shown to occur as part of stable limit cycles. An analysis is developed for these limit cycles that illustrates how they can be predicted.
Limit cycles with chattering in relay feedback systems
 In: Proc. 36th IEEE Conference on Decision and Control
, 1997
"... Abstract—Relay feedback has a large variety of applications in control engineering. Several interesting phenomena occur in simple relay systems. In this paper, scalar linear systems with relay feedback are analyzed. It is shown that a limit cycle where part of the limit cycle consists of fast relay ..."
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Cited by 22 (8 self)
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Abstract—Relay feedback has a large variety of applications in control engineering. Several interesting phenomena occur in simple relay systems. In this paper, scalar linear systems with relay feedback are analyzed. It is shown that a limit cycle where part of the limit cycle consists of fast relay switchings can occur. This chattering is analyzed in detail and conditions for approximating it by a sliding mode are derived. A result on existence of limit cycles with chattering is given, and it is shown that the limit cycles can have arbitrarily many relay switchings each period. Limit cycles with regular sliding modes are also discussed. Examples illustrate the results. Index Terms—Discontinuous control, hybrid systems, nonlinear dynamics, oscillations, relay control, sliding modes. I.
Steady–state and perturbed rhythmical movements: A dynamical analysis.
 Journal of Experimental Psychology: Human Perception and Performance,
, 1991
"... The purpose of this study was to derive the qualitative dynamical properties of a simple type of voluntary rhythmical activity. To this end, rhythmic finger movements were examined in the steadystate and when momentarily perturbed by a torque pulse. It was found that: (a) movement frequency, ampli ..."
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Cited by 20 (1 self)
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The purpose of this study was to derive the qualitative dynamical properties of a simple type of voluntary rhythmical activity. To this end, rhythmic finger movements were examined in the steadystate and when momentarily perturbed by a torque pulse. It was found that: (a) movement frequency, amplitude, and peak velocity were stable under perturbation, signalling the presence of an attractor; and (b) the dimensionality of that attractor, as measured by the correlation integral, was approximately equal to that of the simplest limitcycle oscillators. Also, (c) the strength of the attractor was constant with increasing movement frequency; and (d) the Fourier spectra of the steadystate trials showed an alternating harmonic pattern. These results are consistent with a previouslyderived nonlinear oscillator model. However, (e) the oscillation was phaseadvanced by perturbation overall, and a consistent phasedependent phaseshift pattern occurred. These phaseresponse results are inconsistent with our previous limitcycle model. The overall phaseadvance also shows that any central pattern generator responsible for generating the rhythm must be nontrivially modulated by the limb being controlled.
Modeling and Adaptive Control of Magnetostrictive Actuators
, 1999
"... In this dissertation, we propose a model and formulate a control methodology for a thin magnetostrictive rod actuator. The goal is to obtain a bulk, low dimensional model that can be used for realtime control purposes. Previous and concurrent research in the modeling of magnetostrictive actuators a ..."
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Cited by 18 (2 self)
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In this dissertation, we propose a model and formulate a control methodology for a thin magnetostrictive rod actuator. The goal is to obtain a bulk, low dimensional model that can be used for realtime control purposes. Previous and concurrent research in the modeling of magnetostrictive actuators and the related area of electrostrictive actuators have produced models that are of low order and reproduce their quasistatic response reasonably well. But the main interest in using these and other smart actuators is at a high frequency { for producing large displacements with mechanical rectication, producing sonar signals etc. The well known limitation of smart actuators that are based on electromagnetothermoelastic behaviors of smart materials is the complex, inputrate dependent, hysteretic behavior of the latter. The model proposed in this dissertation, is a bulk model and describes the behaviour of a magnetostrictive actuator by a system with 4 states. We develop this model using phenomenological arguments following the work done by Jiles and Atherton for describing bulk ferromagnetic hysteresis. The model accounts
Virtual Damping and Einstein Relation in Oscillators
 IEEE Journal of SolidState Circuits
, 2003
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Selfoscillations in glycolysis 1. A simple kinetic model
 Eur. J. Biochem
, 1968
"... The paper describes a simple kinetic model of an open monosubstrate enzyme reaction with substrate inhibition and product activation. A comparison between the model and the phosphofructokinase reaction shows a close resemblance between their dynamical properties. This makes it possible to explain q ..."
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Cited by 16 (0 self)
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The paper describes a simple kinetic model of an open monosubstrate enzyme reaction with substrate inhibition and product activation. A comparison between the model and the phosphofructokinase reaction shows a close resemblance between their dynamical properties. This makes it possible to explain qualitatively most experimental data on singlefrequency oscillations in glycolysis. A mathematical analysis of the model has shown the following. 1. I n the model, a t a definite relationship between the parameters, selfoscillations arise. 2. The condition of selfexcitation is satisfied more readily with a lower source rate, larger product sink rate constants, lower productenzyme affinity and higher enzyme activity. 3. Selfoscillations exist only in a certain range of values of the parameter determining the degree of substrate inhibition. This range increases with decreasing source rate. Too strong or, conversely, too weak substrate inhibition leads to damped oscillations. 4. The period of selfoscillations depends on the degree of substrate inhibition, the source rate, the sink rate constant, the enzyme activity, the affinity of the substrate and the product for the enzyme; it decreases with an increase in these values. 5. With an increase in the relative sink rate constant the steady state amplitude of self
Motions and stability of a piecewise holonomic system:the discrete chaplygin sleigh
 Regul. Chaot. Dynamics
, 1999
"... We discuss the dynamics of a piecewise holonomic mechanical system: a discrete sister to the classical nonholonomically constrained Chaplygin sleigh. A slotted rigid body moves in the plane subject to a sequence of pegs intermittently placed and sliding freely along the slot; motions are smooth and ..."
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Cited by 15 (7 self)
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We discuss the dynamics of a piecewise holonomic mechanical system: a discrete sister to the classical nonholonomically constrained Chaplygin sleigh. A slotted rigid body moves in the plane subject to a sequence of pegs intermittently placed and sliding freely along the slot; motions are smooth and holonomic except at instants of peg insertion. We derive a return map and analyze stability of constantspeed straightline motions: they are asymptotically stable if the mass center is in front of the center of the slot, and unstable if it lies behind the slot; if it lies between center and rear of the slot, stability depends subtly on slot length and radius of gyration. As slot length vanishes, the system inherits the eigenvalues of the Chaplygin sleigh while remaining piecewise holonomic. We compare the dynamics of both systems, and observe that the discrete skate exhibits a richer range of behaviors, including coexistence of stable forward and backward motions. 1.
Dynamics of Relay Relaxation Oscillators
, 2001
"... Relaxation oscillators can usually be represented as a feedback system with hysteresis. The relay relaxation oscillator consists of relay hysteresis and a linear system in feedback. The objective of this work is to study the existence of periodic orbits and the dynamics of coupled relay oscillators. ..."
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Cited by 13 (0 self)
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Relaxation oscillators can usually be represented as a feedback system with hysteresis. The relay relaxation oscillator consists of relay hysteresis and a linear system in feedback. The objective of this work is to study the existence of periodic orbits and the dynamics of coupled relay oscillators. In particular, we give a complete analysis for the case of unimodal periodic orbits, and illustrate the presence of degenerate and asymmetric orbits. We also discuss how complex orbits can arise from bifurcation of unimodal orbits. Finally, we focus on oscillators with an integrator as the linear component, and study the entrainment under external forcing, and phase locking when such oscillators are coupled in a ring. I.
Observerbased control of piecewiseaffine systems
 Journal of Control
, 2003
"... This paper presents a new synthesis method for both state and dynamic output feedback control ofa class ofhybrid systems called piecewiseaffine (PWA) systems. The synthesis procedure delivers stabilizing controllers that can be proven to give either asymptotic or exponential convergence rates. The ..."
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Cited by 11 (3 self)
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This paper presents a new synthesis method for both state and dynamic output feedback control ofa class ofhybrid systems called piecewiseaffine (PWA) systems. The synthesis procedure delivers stabilizing controllers that can be proven to give either asymptotic or exponential convergence rates. The synthesis method builds on existing PWA stability analysis tools by transforming the design into a closedloop analysis problem wherein the controller parameters are unknown. More specifically, the proposed technique formulates the search for a piecewisequadratic control Lyapunov function and a piecewiseaffine control law as an optimization problem subject to linear constraints and a bilinear matrix inequality. The linear constraints in the synthesis guarantee that sliding modes are not generated at the switching. The resulting optimization problem is known to be NP hard, but suboptimal solutions can be obtained using the three iterative algorithms presented in the paper. The new synthesis technique allows controllers to be designed with a specified structure, such as a combined regulator and observer. The observers in these controllers then enable switching based on state estimates rather than on measured outputs. The overall design approach, including a comparison ofthe synthesis algorithms and the performance ofthe resulting controllers, is clearly demonstrated in four simulation examples. Paper provisionally accepted for publication in the International Journal of Control.