Finite-time stability and stabilization of nonlinear stochastic hybrid systems

AbstractThis paper deals with the problem of finite-time stability and stabilization of nonlinear Markovian switching stochastic systems which exist impulses at the switching instants. Using multiple Lyapunov function theory, a sufficient condition is established for finite-time stability of the underlying systems. Furthermore, based on the state partition of continuous parts of systems, a feedback controller is designed such that the corresponding impulsive stochastic closed-loop systems are finite-time stochastically stable. A numerical example is presented to illustrate the effectiveness of the proposed method

The Social Influence Enhanced by the Mass Media Broadcasting in Innovation Diffusion

Based on the Bass model and the micro-model of mass media network, we propose an agent-based threshold approach including the mutual interaction between social relationship network and mass media network. Taking the heterogeneity of individuals into account, it is found that the direct advertisement from mass media broadcasting will attract the potential adopters greatly at the beginning of innovation diffusion. In the middle of diffusion process, the previous adopters formalize a positive feedback to the potential adopters via mass media broadcasting. The social collective effect can be strongly enhanced if the potential adopter prefer to mass media broadcasting. Furthermore, it is found that the complexity of the social relationship network may postpone the social collective effect

Reflections on Resumption and Improvement of Enterprise Statement of Profit Distribution

The enterprise profit distribution and its disclosure problem are analyzed to demonstrate why resumption and improvement of the enterprise statement of profitdistribution are needed. It is noted that a limit should be set between disclosures of profit formation and distribution. Resumption of the enterprise statement of profit distribution discloses the conditions of profit distribution in a better way while an improvement helps improve the disclosure of the participation of human capital in enterprise profit distribution. The participation of stakeholders in enterprise profit statement of profit distribution is kept in a “white box” to analyze and studywhether the contribution of production factors matches its participation in distribution

Laser Intensity Noise Suppression for Preparing Audio-Frequency 795 nm Squeezed Vacuum State of Light at Rubidium D1 Line

Laser intensity noise suppression has essential effects on preparation and characterization of the audio-frequency squeezed vacuum state of light based on a sub-threshold optical parametric oscillator (OPO).We have implemented two feedback loops by using relevant acousto-optical modulators (AOM) to stabilize the intensity of 795-nm near infrared (NIR) fundamental laser and 397.5-nm ultraviolet (UV) laser generated by cavity-enhanced frequency doubling.Typical peak-to-peak laser intensity fluctuation with a bandwidth of $\sim10$ kHz in a half hour has been improved from $\pm7.45$$\%$ to $\pm0.06$$\%$ for 795-nm NIR laser beam, and from $\pm9.04$$\%$ to $\pm0.05$$\%$ for 397.5-nm UV laser beam, respectively. The squeezing level of the squeezed vacuum state at 795 nm prepared by the sub-threshold OPO with a PPKTP crystal has been improved from -3.3 to -4.0 dB around 3$\sim$9 kHz of audio analysis frequency range.Comment: 5 pages, 4 figure

A Multi-Pass Optically Pumped Rubidium Atomic Magnetometer with Free Induction Decay

A free-induction-decay (FID) type optically-pumped rubidium atomic magnetometer driven by a radio-frequency (RF) magnetic field is presented in this paper. Influences of parameters, such as the temperature of rubidium vapor cell, the power of pump beam, and the strength of RF magnetic field and static magnetic field on the amplitude and the full width at half maximum (FWHM) of the FID signal, have been investigated in the time domain and frequency domain. At the same time, the sensitivities of the magnetometer for the single-pass and the triple-pass probe beam cases have been compared by changing the optical path of the interaction between probe beam and atomic ensemble. Compared with the sensitivity of ~21.2 pT/Hz^(1/2) in the case of the single-pass probe beam, the amplitude of FID signal in the case of the triple-pass probe beam has been significantly enhanced, and the sensitivity has been improved to ~13.4 pT/Hz^(1/2). The research in this paper provids a reference for the subsequent study of influence of different buffer gas pressure on the FWHM and also a foundation for further improving the sensitivity of FID rubidium atomic magnetometer by employing a~polarization-squeezed light as probe beam, to achieve a sensitivity beyond the photo-shot-noise level.Comment: sensors,2022,22(19):759

On uniqueness of limit cycles in general Bogdanov-Takens bifurcation

In this paper we present a complete study to the well-known Bogdanov-Takens bifurcation and give a rigorous proof for the uniqueness of limit cycles