Series-connection of resonant-tunneling diodes (RTDs) has been considered to be efficient in upgrading the output power when it is introduced to oscillator architecture. This work is for clarifying the same architecture also contributes to increasing oscillation frequency because the device parasitic capacitance is reduced M times for M series-connected RTD oscillator. Although this mechanism is expected to be universal, we restrict the discussion to the recently proposed multiphase oscillator utilizing an RTD oscillator lattice loop. After explaining the operation principle, we evaluate how the oscillation frequency depends on the number of series-connected RTDs through full-wave calculations. In addition, the essential dynamics were validated experimentally in breadboarded multiphase oscillators using Esaki diodes in place of RTDs.

Intrinsic Josephson junctions (IJJs) in the high-Tc cuprate superconductors have several fascinating properties, which are superior to the usual Josephson junctions obtained from conventional superconductors with low Tc, as follows; (1) a very thin thickness of the superconducting layers, (2) a strong interaction between junctions since neighboring junctions are closely connected in an atomic scale, (3) a clean interface between the superconducting and insulating layers, realized in a single crystal with few disorders. These unique properties of IJJs can enlarge the applicable areas of the superconducting qubits, not only the increase of qubit-operation temperature but the novel application of qubits including the macroscopic quantum states with internal degree of freedom. I present a comprehensive review of the phase dynamics in current-biased IJJs and argue the challenges of superconducting qubits utilizing IJJs.

To maintain blockchain-based services with ensuring its security, it is an important issue how to decide a mining reward so that the number of miners participating in the mining increases. We propose a dynamical model of decision-making for miners using an evolutionary game approach and analyze the stability of equilibrium points of the proposed model. The proposed model is described by the 1st-order differential equation. So, it is simple but its theoretical analysis gives an insight into the characteristics of the decision-making. Through the analysis of the equilibrium points, we show the transcritical bifurcations and hysteresis phenomena of the equilibrium points. We also design a controller that determines the mining reward based on the number of participating miners to stabilize the state where all miners participate in the mining. Numerical simulation shows that there is a trade-off in the choice of the design parameters.

Convolutional approximate message-passing (CAMP) is an efficient algorithm to solve linear inverse problems. CAMP aims to realize advantages of both approximate message-passing (AMP) and orthogonal/vector AMP. CAMP uses the same low-complexity matched-filter as AMP. To realize the asymptotic Gaussianity of estimation errors for all right-orthogonally invariant matrices, as guaranteed in orthogonal/vector AMP, the Onsager correction in AMP is replaced with a convolution of all preceding messages. CAMP was proved to be asymptotically Bayes-optimal if a state-evolution (SE) recursion converges to a fixed-point (FP) and if the FP is unique. However, no proofs for the convergence were provided. This paper presents a theoretical analysis for the convergence of the SE recursion. Gaussian signaling is assumed to linearize the SE recursion. A condition for the convergence is derived via a necessary and sufficient condition for which the linearized SE recursion has a unique stationary solution. The SE recursion is numerically verified to converge toward the Bayes-optimal solution if and only if the condition is satisfied. CAMP is compared to conjugate gradient (CG) for Gaussian signaling in terms of the convergence properties. CAMP is inferior to CG for matrices with a large condition number while they are comparable to each other for a small condition number. These results imply that CAMP has room for improvement in terms of the convergence properties.

In our previous work, we developed a quadrotor with a tilting frame using the parallel link mechanism. It can tilt its frame in the pitch direction by driving only one servo motor. However, it has a singularity such that the input torque in the pitch direction equals 0 at ±π/2 tilted state. In this letter, we analyze the Hopf bifurcation of the controlled quadrotor around the singularity and show the stable limit cycle occurs in the pitch direction by simulation and experiments.

This paper studies a novel approach to analysis of switched dynamical systems in perspective of bifurcation and multiobjective optimization. As a first step, we analyze a simple switched dynamical system based on a boost converter with photovoltaic input. First, in a bifurcation phenomenon perspective, we consider period doubling bifurcation sets in the parameter space. Second, in a multiobjective optimization perspective, we consider a trade-off between maximum input power and stability. The trade-off is represented by a Pareto front in the objective space. Performing numerical experiments, relationship between the bifurcation sets and the Pareto front is investigated.

The transition dynamics of a multistable tunnel-diode oscillator is characterized for modulating amplitude of outputted oscillatory signal. The base oscillator possesses fixed-point and limit-cycle stable points for a unique bias voltage. Switching these two stable points by external signal can render an efficient method for modulation of output amplitude. The time required for state transition is expected to be dominated by the aftereffect of the limiting point. However, it is found that its influence decreases exponentially with respect to the amplitude of external signal. Herein, we first describe numerically the pulse generation scheme with the transition dynamics of the oscillator and then validate it with several time-domain measurements using a test circuit.

This letter proposes a numerical method for approximating the location of and dynamics on a class of chaotic saddles. In contrast to the conventional strategy of maximizing the escape time, our proposal is to impose a zero-expansion condition along transversely repelling directions of chaotic saddles. This strategy exploits the existence of skeleton-forming unstable periodic orbits embedded in chaotic saddles, and thus can be conveniently implemented as a variant of subspace Newton-type methods. The algorithm is examined through an illustrative and another standard example.

In this research, we propose an effective stability analysis method to impacting systems with periodically moving borders (periodic borders). First, we describe an n-dimensional impacting system with periodic borders. Subsequently, we present an algorithm based on a stability analysis method using the monodromy matrix for calculating stability of the waveform. This approach requires the state-transition matrix be related to the impact phenomenon, which is known as the saltation matrix. In an earlier study, the expression for the saltation matrix was derived assuming a static border (fixed border). In this research, we derive an expression for the saltation matrix for a periodic border. We confirm the performance of the proposed method, which is also applicable to systems with fixed borders, by applying it to an impacting system with a periodic border. Using this approach, we analyze the bifurcation of an impacting system with a periodic border by computing the evolution of the stable and unstable periodic waveform. We demonstrate a discontinuous change of the periodic points, which occurs when a periodic point collides with a border, in the one-parameter bifurcation diagram.

This report presents experimental measurements of mixed-mode oscillations (MMOs) generated by a weakly driven four-segment piecewise linear Bonhoeffer-van der Pol (BVP) oscillator. Such a roughly approximated simple piecewise linear circuit can generate MMOs and mixed-mode oscillation-incrementing bifurcations (MMOIBs). The laboratory experiments well agree with numerical results. We experimentally and numerically observe time series and Lorenz plots of MMOs generated by successive and nonsuccessive MMOIBs.

The transmission control protocol with a random early detection (TCP/RED) is an important algorithm for a TCP congestion control [1]. It has been expressed as a simple second-order discrete-time hybrid dynamical model, and shows unique and typical nonlinear phenomena, e.g., bifurcation phenomena or chaotic attractors [2], [3]. However, detailed behavior is unclear due to discontinuity that describes the switching of transmission phases in TCP/RED, but we have proposed its analysis method in previous study. This letter clarifies bifurcation structures with it.

This paper studies spike-train dynamics of the bifurcating neuron and its pulse-coupled system. The neuron has periodic base signal that is given by applying a periodic square wave to a basic low-pass filter. As key parameters of the filter vary, the systems can exhibit various bifurcation phenomena. For example, the neuron exhibits period-doubling bifurcation through which the period of spike-train is doubling. The coupled system exhibits two kinds of (smooth and non-smooth) tangent bifurcations that can induce “chaos + chaos = order”: chaotic spike-trains of two neurons are changed into periodic spike-train by the pulse-coupling. Using the mapping procedure, the bifurcation phenomena can be analyzed precisely. Presenting simple test circuits, typical phenomena are confirmed experimentally.

AC conversion has a huge variety of applications and so there are many ongoing research topics as in every type of power electronic conversion. New semiconductors allow the increase of the switching frequency fact that brings a whole new prospective improvement in converter's operation. Many other possible nonlinear operation regimes, including period doubling and chaotic oscillations, appear besides the conventional steady state operation. In this work, a nonlinear discrete-time model of an AC/AC buck type converter is proposed. A discrete time iterative map is derived to highlight the sensitive switching dynamics. The model is able to observe fast scale phenomena and short transient effects. It offers more information compared to other methods such as the averaging ones. According to Electro-Magnetic Compatibility (EMC) regulations, low wide-band noise is more acceptable than the high narrow-band, therefore the goal of this work is to spread the harmonic noise into a wide frequency spectrum which has lower amplitudes compared to the conventional comb-like spectrum with distinctive amplitudes at switching frequency multiples. Through the numerical and experimental consideration the converter can operate in a chaotic motion and the advantages of the performance improvement are also discussed.

This paper proposes the physical architecture of an electric power system with multiple homes. The notion of home is a unit of small-scale power system that includes local energy source, energy storage, load, power conversion circuits, and control systems. An entire power system consists of multiple homes that are interconnected via a distribution network and that are connected to the commercial power grid. The interconnection is autonomously achieved with a recently developed technology of grid-connected inverters. A mathematical model of slow dynamics of the power system is also developed in this paper. The developed model enables the evaluation of steady and transient characteristics of power systems.

This letter studies a digital return map that is a mapping from a set of lattice points to itself. The digital map can exhibit various periodic orbits. As a typical example, we present the digital logistic map based on the logistic map. Two fundamental results are shown. When the logistic map has a unique periodic orbit, the digital map can have plural periodic orbits. When the logistic map has an unstable period-3 orbit that causes chaos, the digital map can have a stable period-3 orbit with various domain of attractions.

A generalized version of sequential logic circuit based neuron models is presented, where the dynamics of the model is modeled by an asynchronous cellular automaton. Thanks to the generalizations in this paper, the model can exhibit various neuron-like waveforms of the membrane potential in response to excitatory and inhibitory stimulus. Also, the model can reproduce four groups of biological and model neurons, which are classified based on existence of bistability and subthreshold oscillations, as well as their underlying bifurcations mechanisms.

This paper clarifies the bifurcation structure of the chaotic attractor in an interrupted circuit with switching delay from theoretical and experimental view points. First, we introduce the circuit model and its dynamics. Next, we define the return map in order to investigate the bifurcation structure of the chaotic attractor. Finally, we discuss the dynamical effect of switching delay in the existence region of the chaotic attractor compared with that of a circuit with ideal switching.

A generalized version of a piece-wise constant (ab. PWC) spiking neuron model is presented. It is shown that the generalization enables the model to reproduce 20 activities in the Izhikevich model. Among the activities, we analyze tonic bursting. Using an analytical one-dimensional iterative map, it is shown that the model can reproduce a burst-related bifurcation scenario, which is qualitatively similar to that of the Izhikevich model. The bifurcation scenario can be observed in an actual hardware.

This paper presents pulse-coupled piecewise constant spiking oscillators (PWCSOs) consisting of two PWCSOs and a coupling method is master-slave coupling. The slave PWCSO exhibits chaos because of chaotic response of the master one. However, if the parameter varies, the slave PWCSO can exhibit the phenomena as a periodicity in the phase plane. We focus on such phenomena and corresponding bifurcation. Using the 2-D return map, we clarify its mechanism.

This paper studies a switched dynamical system based on the boost converter with a solar cell input. The solar cell is modeled by a piecewise linear current-controlled voltage source. A variant of peak-current-controlled switching is used in the boost converter. Applying the mapping procedure, the system dynamics can be analyzed precisely. As a main result, we have found an important example of trade-off between the maximum power point and stability: as a parameter (relates to the clock period) varies, the average power of a periodic orbit can have a peak near a period-doubling bifurcation set and an unstable periodic orbit can have the maximum power point.