Global Stability in Dynamical Systems with Multiple Feedback Mechanisms

A class of n-dimensional ODEs with up to n feedbacks from the n’th variable is analysed. The feedbacks are represented by non-specific, bounded, non-negative C1 functions. The main result is the formulation and proof of an easily applicable criterion for existence of a globally stable fixed point of the system. The proof relies on the contraction mapping theorem. Applications of this type of systems are numerous in biology, e.g., models of the hypothalamic-pituitary-adrenal axis and testosterone secretion. Some results important for modelling are: 1) Existence of an attractive trapping region. This is a bounded set with non-negative elements where solutions cannot escape. All solutions are shown to converge to a “minimal” trapping region. 2) At least one fixed point exists. 3) Sufficient criteria for a unique fixed point are formulated. One case where this is fulfilled is when the feedbacks are negative.

Method for in situ calibration of multiple feedback interferometers

A method is presented for in situ resolution calibration of multiple feedback interferometers(MFIs) using two lasers with di?erent feedback levels simultaneously. The laser with weak optical feedback level generates half-wavelength optical fringes, whereas the laser with strong multiple feedback level generates optical nanofringes. By using this method, the number of displaced optical nano-fringes can be easily counted, and the resolution of the MFIs can be accurately determined. The integrated MFIs can be used to measure displacements and calibrate other displacement sensors.

Reliability Analysis of Repairable System with Multiple Closed-Loop Feedbacks Based on GO Method

In order to solve the problem of reliability modeling and the analysis of complex systems with multiple closed-loop feedbacks,a new reliability analysis method for repairable systems with multiple closed-loop feedbacks is proposed based on the goal-oriented(GO)methodology.Firstly,the basic theories and advantages of GO method are introduced.Secondly,a type-24B multiple closed-loop feedback structure operator is proposed through GO method with its operation formula given,which expands the types of GO method operators and the application scope of their reliability analysis.Finally,taking a certain type of diesel engine fuel supply system an example,the quantitative and qualitative analysis is carried out through GO method,Monte Carlo simulation as well as FTA respectively.The availability results verify the availability of the proposed type-24B operator in the reliability analysis of multiple closed-loop feedback systems.The qualitative analysis results indicate the accuracy and usability of the GO method as a qualitative analysis method.

Intensity modulation in single-mode microchip Nd：YAG lasers with asymmetric external cavity

Intensity modulation induced by the asymmetric external cavity in single-mode microchip Nd：YAG lasers is prosented. Two kinds of experimental results are discussed based on multiple feedback effects. In one case, the intensity modulation curve is a normal sine wave, whose fringe frequency is four times higher than that of a conventional optical feedback system, caused by multiple feedback effects. In the other case, the intensity modulation curve is the overlapping of the above quadruple-frequency signal and conventional optical feedback signal, which is determined by the additional phase difference induced by the asymmetric external cavity. The theoretical analyses are in good agreement with the experimental results. The quadruple-frequency modulation of the laser output intensity can greatly increase the resolution of displacement measurement of an optical feedback system.