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The stochastic Phase-Locked Loop (PLL) system, a non-linear dynamic circuit, is an appealing and non-trivial case in the general theory of dynamical systems. In this paper, the stochastically-influenced PLL system is the subject of investigation in lieu of the noise-free case. Significantly, Stochastic Differential Equation (SDE) descriptions refine estimation algorithms, stability conditions and...
The noise-free CMOS inverter is described by a first- order non-linear differential equation that can be regarded as a standard case in electronic circuits from the system-theoretic viewpoint. In lieu of the noise-free CMOS inverter, this paper explains the stochastic CMOS inverter at the low power supply voltage. The method of this paper utilizes the Kolmogorov-Fokker-Planck equation for the noise...
In this paper, we present the noise analysis of simple, but an appealing resistor-capacitor series circuit. As it has found applications in many circuits like RC filter in phase locked loop. The noise originates from the arbitrary thermal motion of carriers and the discreteness of charge. Noise signals are random and must be treated by statistical means. Even though we cannot predict the real noise...
Flexible needles with bevel tips are being developed as useful tools for minimally invasive surgery and percutaneous therapy. When such a needle is inserted into soft tissue, it bends due to the asymmetric geometry of the bevel tip. This insertion with bending is not completely repeatable. We characterize the deviations in needle tip pose (position and orientation) by performing repeated needle insertions...
This paper discusses two regime-switching TARX models for electricity prices that include spikes, antispikes and microeconomic threshold effects typical of power markets, without using jumps. Preliminary version.
The Lyapunov equation, which describes stochastic variations of systems as a covariance equation, plays a central role in evaluation and prediction of behavior of genetic regulatory networks fluctuated by molecular noises. When the genetic network is an autonomously oscillatory system, the Lyapunov equation becomes a periodic differential equation that has generally unbounded solutions. We discuss...
Circadian rhythms, which are observed in most of organisms, e.g. bacteria, fungi, plants, and animals, are self-sustained oscillations with about 24 hours period and a remarkable temperature compensation property. By using the temperature-compensated and robust temperature-compensated deterministic models for circadian rhythms, we perform the stochastic simulations based on the Gillespie's method...
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