stochastic

摘要： It has recently been demonstrated experimentally that a turbulent plasma created by the collision of two inhomogeneous,asymmetric,weakly magnetized,laser-produced plasma jets can generate strong stochastic magnetic fields via the small-scale turbulent dynamo mechanism,provided the magnetic Reynolds number of the plasma is sufficiently large.In this paper,we compare such a plasma with one arising from two pre-magnetized plasma jets whose creation is identical save for the addition of a strong external magnetic field imposed by a pulsed magnetic field generator.We investigate the differences between the two turbulent systems using a Thomson-scattering diagnostic,x-ray selfemission imaging,and proton radiography.The Thomson-scattering spectra and x-ray images suggest that the external magnetic field has a limited effect on the plasma dynamics in the experiment.Although the external magnetic field induces collimation of the flows in the colliding plasma jets and although the initial strengths of the magnetic fields arising from the interaction between the colliding jets are significantly larger as a result of the external field,the energies and morphologies of the stochastic magnetic fields post-amplification are indistinguishable.We conclude that,for turbulent laser-plasmas with supercritical magnetic Reynolds numbers,the dynamo-amplified magnetic fields are determined by the turbulent dynamics rather than the seed fields or modest changes in the initial flow dynamics of the plasma,a finding consistent with theoretical expectations and simulations of turbulent dynamos.

摘要： In this paper,a deterministic and stochastic fractional-order model of the tri-trophic food chain model incorporating harvesting is proposed and analysed.The interaction between prey,middle predator and top predator population is investigated.In order to clarify the characteristics of the proposed model,the analysis of existence,uniqueness,non-negativity and boundedness of the solutions of the proposed model are examined.Some sufficient conditions that ensure the local and global stability of equilibrium points are obtained.By using stability analysis of the fractional-order system,it is proved that if the basic reproduction number R_(0)<1,the predator free equilibrium point E_(1) is globally asymptotically stable.The occurrence of local bifurcation near the equilibrium points is investigated with the help of Sotomayor’s theorem.Some numerical examples are given to illustrate the theoretical findings.The impact of harvesting on prey and themiddle predator is studied.We conclude that harvesting parameters can control the dynamics of the middle predator.A numerical approximation method is developed for the proposed stochastic fractional-order model.

摘要： Operators of renewable energy systems (RESs) must always manage uncertainty to some extent to ensure the reliability and the security of the electric power supply source. The guiding principle in this regard is to ensure service reliability and quality by balancing load variations with the variable renewable energy (VRE) sources. If the power generated by these VRE sources is not properly managed in conjunction with the varying load, the power grid may fail to achieve the required balance. To ensure its reliable operation, reliability analysis is vital for wind energy generation system (WEGS). This paper evaluated and assessed the reliability of WEGS and a proposed varying load by first using a stochastic approach to model the WEGS and the proposed varying load after which power generation indices were used to evaluate and assess the performance of the model. The WEGS and the varying load were modelled separately after which the two were combined into one model. Full availability, partial availability, the expected energy not supplied (EENS) or loss of energy expectation (LOEE), the mean or average instantaneous electric power generation and mean instantaneous generation deficiency were the indices used for the evaluation of the WEGS. The results indicated that the electric power generation will meet the power demand during most of the transition states of the WEGS with the expectation that the variation in the load will not be at fast pace and in large quantum.

摘要： A criterion on a repeller being a null set of any limit measure for stochastic differential equations Lifeng Chen,Zhao Dong&Jifa Jiang Abstract This paper studies limit behaviors of stationary measures for stochastic ordinary differential equations with nondegenerate noise and presents a criterion to guarantee that a repeller with zero Lebesgue measure is a null set of any limit measure.Using this criterion,we first provide a series of nontrivial concrete examples to show that their repelling limit cycles or quasi-periodic orbits are null sets for all limit measures.

摘要： Dear editor,Fault diagnosis of industrial production processes are crucial for early detection of abnormal conditions and help operators to prevent accidents in a timely manner.Therefore,reasonably establishing a fault diagnosis model with better performance and reducing false alarm rate are vital for improving the efficiency of industrial operations and ensuring the safety and reliable operation of equipment.

摘要： Dear editor,To improve the safety and reliability of industrial processes,fault-detection problems in dynamic systems have attracted increasing research attention[1].On the one hand,to enhance fault sensitivity,applying the H-performance index to measure the minimum impact of the fault on the residual signal has been proposed.On the other hand.

摘要： Dear editor,The stochastic singular system is also called the stochastic differential algebraic system,stochastic descriptor system,generalized stochastic system,and stochastic degenerate system(e.g.,[1–4]).This type of system is found in numerous fields of application,which include fluid dynamics,the modeling of multi-body mechanisms,finance,inputoutput economics and the problem of protein folding.The theory of stochastic singular systems,in which a special class of linear stochastic singular systems is considered,has been developed recently[1].The form of the initial function is given,so the corresponding initial value problem is uniquely solvable by applying the theory of generalized stochastic processes.Using white noise and fractional white noise.

摘要： Dear editor,In the field of applied mathematics and control theory,the research on stochastic Markovian jump systems has attracted increasing attention in recent years.A few studies have been conducted on stochastic Markovian jump systems[1-6].Most previously conducted studies on stochastic Markovian jump systems investigate the discrete timevarying delay[4-6],whereas the distributed delay has not been given much attention owing to the difficulties involved in applying mathematical analysis.

摘要： NANOGrav has recently reported the detection of a common-spectrum process via the time-of-arrival data of 47 millisecond pulsars[1],which could be interpreted by a stochastic gravitational wave background(SGWB)in the nanohertz frequency band(f∼10−9 Hz)with energy density parameterΩGW∼10−9.Despite the vague quadrupole correlation that obstructs the identification of gravitational waves,this report hints the possibility of some new physics at around or below 100 MeV that can generate nanohertz gravitational waves by,for instance,the first order phase transition(FOPT).

摘要： The pedestrian-induced lateral vibration of footbridges is essentially classified as a nonlinear stochastic vibration.Accordingly,bridge vibration stability falls within the field of nonlinear stochastic vibration stability.At present,the Lyapunov method is mainly used to analyze such stability.However,this method is qualitative,and it cannot quantitatively analyze the vibration stability probability.In this study,a new analytical method based on a comparison of the input energy and the variation of intrinsic energy(IEVIE)is used to analyze the nonlinear stochastic vibration stability of the lateral vibration of the footbridge.The improved Nakamura model is used to describe the lateral nonlinear stochastic vibration of the footbridge.A combination of the IEVIE method and the probability density evolution(PDE)method is then proposed,in which the IEVIE method is utilized to determine vibration stability.The PDE method is used to obtain the reliability of vibration stability.The proposed method is successfully applied to the Millennium Bridge,and its effectiveness is verified by comparing the Monte Carlo and Lyapunov methods.The proposed method can obtain the dynamic probability of the vibration as stable or instable and provide a reference for quantitative analysis of lateral nonlinear stochastic vibration stability of footbridges.

摘要： An average consensus protocol is proposed for discrete-time double-integrator multi-agent systems with communication noises under fixed topologies. The proposed consensus protocol is composed of two parts: the agent's own state feedback and the relative states between the agent and its neighbor agents. Due to the existence of communication noises, the relative states cannot be obtained accurately. To attenuate the noise effect, a time-varying consensus gain a(k) is applied to the relative states in the proposed protocol. Hence, the closed-loop dynamics of multi-agent systems is a linear stochastic difference equation with variable coefficients. Fortunately, the state transition matrix of this stochastic system can be solved, and the dynamical behavior of linear multi-agent systems can therefore be determined. It is proved that the proposed protocol is able to solve the mean square average consensus problem if and only if the topology graph is connected; and the time-varying gain a(k) satisfies the stochastic-approximation type conditions (Omission)。