Yusuke Matsuoka

PIECEWISE CONSTANT SWITCHED DYNAMICAL SYSTEMS IN POWER ELECTRONICS

This paper overviews nonlinear dynamics of switching power converters which are common objects in dynamical system theory and power electronics. First, complex dynamics of single switching power converters is discussed. Their nonlinear switching can cause rich chaotic and bifurcation phenomena including complicated superstable periodic behavior in discontinuous conduction mode. Second, paralleled converters with winner-take-all switching is discussed. This system can realize multiphase synchronization relating to current sharing with smaller ripple for low-voltage high-current capabilities. Analysis of the dynamics is performed through simple models having piecewise constant vector field and piecewise linear trajectories. Third, simple hardware implementation method is shown and typical phenomena are confirmed experimentally. Finally some future problems are discussed.

A Simple Chaotic Spiking Oscillator Having Piecewise Constant Characteristics

This paper studies a chaotic spiking oscillator consisting of two capacitors, two voltage-controlled current sources of signum shape and one impulsive switch. The vector field of circuit equation is piecewise constant and embedded return map is piecewise linear. Using the map parameter condition for chaos generation is given. Using a simple test circuit typical phenomena can be confirmed experimentally.

Rich Superstable Phenomena in a Piecewise Constant Nonautonomous Circuit with Impulsive Switching

This paper studies rich superstable phenomena in a nonautonomous piecewise constant circuit including one impulsive switch. Since the vector field of circuit equation is piecewise constant, embedded return map is piecewise linear and can be described explicitly in principle. As parameters vary the map can have infinite extrema with one flat segment. Such maps can cause complicated periodic orbits that are superstable for initial state and are sensitive for parameters. Using a simple test circuit typical phenomena are verified experimentally.

Rotation Map with a Controlling Segment: Basic Analysis and Application to A/D Converters

This paper studies the rotation map with a controlling segment. As a parameter varies, the map exhibits superstable periodic orbits, chaos and rich bifurcation phenomena. The map is applicable to an A/D converter having efficient resolution characteristics. The converter can be realized as a circuit model based on a spiking neuron and the rate-coding. Presenting a test circuit, basic operation is confirmed experimentally.

Rotation map with a controlling segment and its application to A/D converters

This paper studies the rotation map with a controlling segment. As the segment varies, the map exhibits superstable periodic orbits, chaos and related bifurcation. The map is applicable to an A/D converter having efficient resolution characteristics. We then present a circuit model of the A/D converter based on spiking neuron and rate-coding. Presenting a test circuit, basic operation is confirmed experimentally.

A piecewise constant switched chaotic circuit with rect-rippling return maps

This paper studies a switched chaotic circuit with periodic pulse-train input. The vector field of the circuit equation is piecewise constant and the embedded return maps are piecewise linear: it is well suited for theoretical analysis. First we overview basic dynamics and rich chaotic and periodic behavior. We then focus on a parameter subspace and show interesting phenomena: the return map can fluctuate and the chaotic attractor is changed into complicated super-stable periodic attractors. Typical phenomena can be confirmed experimentally.

Analysis of inter-spike interval characteristics of piecewise constant chaotic spiking oscillators

This paper studies dynamics of a simple chaotic spiking oscillator having piecewise constant characteristics. The state variable can vibrate and is reset to the base level just after it reaches the threshold. Repeating this vibrate-and-fire behavior, rich chaotic spike-trains can be generated. Since the solution and return map are piecewise linear, precise analysis is possible. We have investigated characteristics of inter-spike intervals (ISIs) and have found interesting properties: rdquoThe system can output chaotic spike-trains characterized by line-like spectrums of ISIs. Such phenomena and chaos with continuous spectrum appear alternately and make window-like structure in the parameter space. The continuous spectrum of chaos can have wider-band than other types of spiking oscillators.rdquo Presenting a simple electric circuit, typical phenomena are confirmed experimentally.

Complicated superstable behavior in a piecewise constant circuit with impulsive switching

This paper studies superstable phenomena in a simple circuit consisting of two capacitors, two signum voltage-controlled current sources and one time-controlled impulsive switch. The circuit equation defines piecewise constant vector field, the trajectory is piecewise linear, and the embedded return map is piecewise linear: it is well suited for precise analysis. In some parameter range the map has infinite extrema and one flat segment. In this case the circuit exhibits extremely complicated periodic orbits characterized by superstability for initial value, very fast transient and sensitivity for parameters