The orbital portrait of quasi-periodic oscillation shows transition like change with the amplitude of external force in periodically forced van der Pol oscillator. This phenomenon originates from frequency pulling between self-sustained and periodic external oscillations induced by the frequency shift of former. We estimate this shift and succeed in deriving the transition points at which the portrait changes.

Variation of bifurcation diagram of difference equation, X (t1) AX (t)(1X (t) BX (t1) ), investigated as a function of B. Several bifurcation patterns appear with B, such as logistic model like pattern, period-3, period-4 and oscillatory pattern.

A single chip MPEG2 MP@HL Video decoder has been developed, which consists mainly of specific functional units and macroblock level pipeline buffers. A new organization is also devised for a set of off-chip frame memories and the interfaces associated with it. Owing to sophisticated I/O interfaces among functional units, the macroblock level pipeline in conjunction with different decording facilities attains a high throughput to such an extent as to decode HDTV images in real time. Moreover, a set of these functional units, pipeline buffers, and frame memory interfaces, together with a sequence controller, is integrated for the first time in a single chip, which has the total area of 8.8 9.2mm2 with a 0.6µm triple-mental CMOS technology, and dissipates 1.2 W from a single 3.3 V supply.

Quasi-periodic or harmonic oscillation transforms into fundamental oscillation as external force increases in forced van der Pol oscillator. Numerical analyses reveal that quasi-periodic or harmonic oscillation can exist metastably in a finite time interval even in a region where fundamental oscillation is stable, which has not been predicted theoretically.

In the delayed regulation medel, X(t+1)=AX(t){1-X(t-1)}, new bifurcation regions which have been overlooked in the past studies were found out for -1.01A0 and 2.27563A2.2838. In the former fixed point lying at 0 is destabilized at A=-1, and new type bifurcation is induced for A-1, where oscillation with saw-tooth waveform is observed. In the latter the stability once lost for A2.271 is restored for A2.27563, and the stable region continues up to A=2.2838.

The dynamics is investigated on the delayed regulation model under period-2 perturbation described as x(t+1)={A+(-1)te}x(t){1-x(t-1)}, t=1, 2, 3 . . . The e-dependences of the bifurcation points are analyzed through usual stability analysis of fixed point and periodic solution, however one of them is derived through the stability analysis of the "virtual" period-2 solution.

Usually periodic behaviour can be hardly seen in quasi-periodic oscillation, r1 cos ω1tr2 cos ω2t, when ω1/ω2 is not simple rational number, however we succeed in finding out new type oscillatory behaviour of it in the point at which the amplitude is extremum.

This paper proposes a transparent glass quartz antenna for 5G-millimeter-wave-connected vehicles and clarifies the characteristics of signal reception when the glass antennas are placed on the windows of a vehicle traveling in an urban environment. Synthetic fused quartz is a material particularly suited for millimeter-wave devices owing to its excellent low transmission loss. Realizing synthetic fused quartz devices requires accurate micromachining technology specialized for the material coupled with the material technology. This paper presents a transparent antenna comprising a thin mesh pattern on a quartz substrate for installation on a vehicle window. A comparison of distributed transparent antennas and an omnidirectional antenna shows that the relative received power of the distributed antenna system is higher than that of the omnidirectional antenna. In addition, results show that the power received is similar when using vertically and horizontally polarized antennas. The design is verified in a field test using transparent antennas on the windows of a real vehicle.

The effects of external noise on lifetime of metastable oscillation mode observed in forced van der Pol oscillator are investigated to clarify the origin of destablization of the modes. The noise is found to suppress the stability of the mode when the noise is intense enough compared with the fluctuation inherent to the oscillator.

Stationary solution analysis shows a transition from quasi-periodic to fundamental oscillations at critical external force strength, Ec when the external periodic force increases in self-sustained hard-mode oscillation equation. But detailed numerical analysis reveals another critical external force, (Ec). For E quasi-periodic, and for EEc fundamental oscillations exist stably, however amplitude modulated oscillation is observed in the transition region EEc.

Transition phenomena associated with synchronization are investigated between van der Pol and hard-mode oscillators with slightly different frequencies interacting through linear coupling. Three types transitions between asynchronous and synchronous states appear, and power law divergence of time describing the transition is observed near the transition point.

It is well know that charges stored in condenser decay exponentially in time through resistor in CR-circuit. But in some types of condensers the exponential decay at initial stage breakes down, and the speed of discharge slows down. There the decay has long time tail characteristic to fractal time random walk.

The oscillatory-nonoscillatory transition is induced in blocking oscillator by controlling the source bias voltage. The oscillation peried shows logarhythmic divergence near the critical bias where the fluctuation of it also becomes remarkable. Its standard deviation is expressed by power law with critical index of 0.33.