This letter studies a pulse-coupled system constructed by delayed cross-switching between two bifurcating neurons. The system can exhibit an interesting bifurcation: the delay-coupling can change chaotic behavior of single neurons into stable periodic behavior. Using the 1D phase map, it is clarified that the phenomenon is caused by the tangent bifurcation for the delay parameter. Presenting a simple test circuit, the phenomenon can be confirmed experimentally.

This paper studies switched dynamical systems based on a simplified model of two-paralleled dc-dc buck converters in current mode control. In the system, we present novel four switching rules depending on both state variables and periodic clock. The system has piecewise constant vector field and piecewise linear solutions: they are well suited for precise analysis. We then clarify parameter conditions that guarantee generation of stable 2-phase synchronization and hyperchaos for each switching rule. Especially, it is clarified that stable synchronization is always possible by proper use of the switching rules and adjustment of clock period. Presenting a simple test circuit, typical phenomena are confirmed experimentally.

This paper studies a simple spiking oscillator having piecewise constant vector field. Repeating vibrate-and-fire dynamics, the system exhibits various spike-trains and we pay special attention to chaotic spike-trains having line-like spectrum in distribution of inter-spike intervals. In the parameter space, existence regions of such phenomena can construct infinite window-like structures. The system has piecewise linear trajectory and we can give theoretical evidence for the phenomena. Presenting a simple test circuit, typical phenomena are confirmed experimentally.

In this paper, we investigate the transitional dynamics and quasi-periodic solution appearing after the Saddle-Node (SN) bifurcation of a periodic solution in an inductor-coupled asymmetrical van der Pol oscillators with hard-type nonlinearity. In particular, we elucidate, by investigating global bifurcation of unstable manifold (UM) of saddles, that transitional dynamics and quasi-periodic solution after the SN bifurcation appear based on different structure of UM.

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.

This paper studies a spiking neuron circuit with triangular base signal. The circuit can output rich spike-trains and the dynamics can be analyzed using a one-dimensional piecewise linear map. This system exhibits period doubling bifurcation, tangent bifurcation, super-stable periodic orbit bifurcation and so on. These phenomena can be characterized based on the inter-spike intervals. Using the maps, we can analyze the phenomena precisely. By presenting a simple test circuit, typical phenomena are confirmed experimentally.

This paper studies nonlinear dynamics of a simplified model of multiple-input parallel buck converters. The dynamic winner-take-all switching is used to achieve N-phase synchronization automatically, however, as parameters vary, the synchronization bifurcates to a variety of periodic/chaotic phenomena. In order to analyze system dynamics we adopt a simple piecewise constant modeling, extract essential parameters in a dimensionless circuit equation and derive a hybrid return map. We then investigate typical bifurcation phenomena relating to N-phase synchronization, hyperchaos, complicated superstable behavior and so on. Ripple characteristics are also investigated.

Buck, boost, and buck-boost converters constitute large class of dc-dc converters used in practice and are interesting nonlinear dynamical systems. It has been shown earlier that various nonlinear phenomena including subharmonics and chaos can be observed in these converters. In this paper we show that with the simplifying assumption that voltage regulation is achieved in high frequency modulation, a very simple dimensionless model can be derived that explains the dynamic phenomena in both continuous conduction mode as well as the discontinuous conduction mode. Using this model, we analyze some peculiar aspects of the dynamics in discontinuous conduction mode like the occurrence of superstable orbits.

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.

In this paper, we propose a variational method to derive the coefficients of piecewise-linear (PWL) models able to accurately approximate nonlinear functions, which are vector fields of autonomous dynamical systems described by continuous-time state-space models dependent on parameters. Such dynamical systems admit limit cycles, and the supercritical Hopf bifurcation normal form is chosen as an example of a system to be approximated. The robustness of the approximations is checked, with a view to circuit implementations.

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.

In this paper, we propose a modified bursting neuron model, which is a natural extension of an original one proposed by the author et al. We will show that chaotic bursts appear in the modified model though there exhibit quasi-periodic bursts in the original one. Moreover, we will show that such chaotic bursts appear by breaking down a pair of invariant closed curves, which is generated by a Hopf bifurcation for a pair of two-periodic points.

The resource allocation problem in multi-agent systems is one of the crucial problems hindering the development of multi-agent technologies. This study demonstrates that "time delay" functions as an effective factor in a resource allocation, contrasting to the conventional real-time oriented multi-agent paradigm by 1) introducing a "fickle" agent, whose own strategy fluctuates randomly, and 2) an agent repository mechanism. This study also demonstrates that in the resource allocation process, time delay induces dramatic changes in performance, the specific phenomenon is the so-called "phase transition phenomenon". This finding means emergence of the phase transition is cited as a major factor governing multi-agent system performance. This knowledge is of essential importance in the regulation in multi-agent performance.

This letter studies a simple nonautonomous chaotic circuit constructed by adding an impulsive switch to the RCL circuit. The switch operation depends on time and on state variable through a refractory threshold. The circuit exhibits various chaotic attractors, periodic attractors and related bifurcation phenomena. The dynamics can be analyzed using 1-D return map focusing on the time-dependent switching moments. Using a simple test circuit model typical phenomena are verified in PSPICE simulations.

This paper studies dynamics of a delta modulator for PWM control. In order to analyze the circuit dynamics we derive a one-dimensional return map of switching time. The map is equivalent to a circle map in wide parameter region and its nonperiodic behavior corresponds to undesired asynchronous operation of the circuit. We then present a simple stabilization method of the system operations by means of periodic compulsory switching. The mechanism of the stabilization is considered from viewpoints of bifurcation. Using a simple test circuit, typical operations are confirmed experimentally.

In this paper, we examine oscillatory modes generated by the Hopf bifurcations of equilibrium points except for the origin in a system of coupled four oscillators. (The bifurcation analyses of the origin for many coupled oscillators were already done.) The Hopf bifurcations of the equilibrium points with strong symmetrical property and the generated oscillatory modes are classified. We observe four-phase, in-phase and a pair of anti-phase synchronized states. Even in a system of four coupled oscillators, we discover the existence of a stable three-phase oscillation. By the numerical bifurcation analysis of generated periodic oscillations we find out successive period-doubling bifurcations as the route to chaos and show some of them are symmetry-breaking bifurcations. As a result of the symmetry-breaking period-doubling bifurcations, a periodic solution with complete synchronization becomes a chaotic solution with phase synchronization.

This paper presents pulse-coupled two bifurcating neurons. The single neuron is represented by a spike position map and the coupled neurons can be represented by a composition of the spike position maps. Using the composite map, we can analyze basic bifurcation phenomena and can find some interesting phenomena that are caused by the pulse-coupling and are impossible in the single neuron. Presenting a simple test circuit, typical phenomena are confirmed experimentally.

New Recommendation and Future Standards highlight the Power Factor Correction (PFC) converter as a basic requirement for switching power supplies. Most high-frequency power factor correctors use resistor emulation to achieve a near-unity power factor and a small line current distortion. This technique requires forcing the input current with an average-current-mode control to follow the input voltage. Stability of this system was discussed previously by using some linear models. However, in this paper, two nonlinear phenomena have been encountered in the PFC circuit, period doubling bifurcation and chaos. Detection of these new instability phenomena in the stable regions predicted by the prior linear PFC models makes us more susceptible towards them, and reveals the need to consider a nonlinear models. A nonlinear model performing the practical operation of a boost PFC converter has been developed. Then, a simplified and accurate nonlinear model has been proposed and verified experimentally. As a result from this model, instability maps have been introduced to determine the boundary between stable and unstable operating ranges. Then, the period doubling bifurcation has been studied through a new proposed technique based on the capacitor storage energy. It is cleared that, As the load lessens, a required extra storage power is needed to achieve the significant increase in the output voltage. Then, if the PFC system can provide this extra energy, the operation can reach stability with new zero-storage energy else the system will have double-line zero energy that is period doubling bifurcation.

A stability of the cascade two-stage Power-Factor-Correction converter is investigated. The first stage is boost PFC converter to achieve a near unity power factor and the second stage is forward converter to regulate the output voltage. Previous researches studied the system using linear analysis. However, PFC boost converter is a nonlinear circuit due to the existence of the multiplier and the large variation of the duty cycle. Moreover, the effect of the second stage DC/DC converter on the first stage PFC converter adds more complexity to the nonlinear circuit. In this issue, low-frequency instability has been detected in the two-stage PFC converter assuring the limitation of the prior linear models. Therefore, nonlinear model is proposed to detected and explain these instabilities. The borderlines between stable and unstable operation has been made clear. It is cleared that feedback gains of the first stage PFC and the second stage DC/DC converters are the main affected parts to the total system stability. Then, a simplified nonlinear model is provided. Experiment confirm the two models with a good agreement. These nonlinear models have introduced new PFC design scheme by choosing the minimum required output capacitor and the feedback loop design.

From the bifurcation viewpoint, this study examines a boost PFC converter with average-current-mode control. The boost PFC converter is considered to be a nonlinear circuit because of its use of a multiplier and its large duty cycle variation for input current control. However, most previous studies have implemented linear analysis, which ignores the effects of nonlinearity. Therefore, those studies were unable to detect instability phenomena. Nonlinearity produces bifurcations and chaos when circuit parameters change. The classical PFC design is based on a stable periodic orbit that has desired characteristics. This paper describes the main bifurcations that this orbit may undergo when the parameters of the circuit change. In addition, the instability regions in the PFC converter are delimited. That fact is of practical interest for the design process. Moreover, a prototype PFC circuit is introduced to examine these instability phenomena experimentally. Then, a special numerical program is developed. Bifurcation maps are provided based on this numerical study. They give a comprehensive outstanding for stability conditions and identify stable regions in the parameter space. Moreover, these maps indicate PFC converter dynamics, power factors, and regulation. Finally, numerical analyses and experimentation show good agreement.