Best performance analysis for stochastic perturbation systems with spectral factorization

We investigate the best performance for linear feedback control systems in the case that plant uncertainty is to be considered. First, we define an average integral square criterion of tracking error over a class of stochastic model errors. By utilizing spectral factorization to minimize the performance index, we derive an optimal controller design method and further study best performance in the presence of stochastic perturbation. The results can be used to evaluate optimal performance in practical control system designs.

Some Further Results on Fixed-Time Synchronization of Neural Networks with Stochastic Perturbations

In this paper, fixed-time (FXT) synchronization issue of a type of neural networks (NNs) with stochastic perturbations is considered. First, we obtained some novel sufficient criteria to guarantee the FXT synchronization of considered networks via introducing two types of controllers and employing some inequality techniques. Lastly, our theoretical results are verified via giving two numerical examples with their Matlab simulations.

The Impact of Nonlinear Stochastic Perturbation on Dynamical Behavior of an HIV Infection System

In this paper,the authors develop and study an HIV infection system with two distinct cell subsets and nonlinear stochastic perturbation.Firstly,the authors obtain that the solution of the system is positive and global.Secondly,for the corresponding linear case,the authors derive a critical condition R0S similar to deterministic system.When R0S>1,the authors establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution to the stochastic system,respectively.Finally,the authors give sufficient criterions for extinction of the diseases.The proposed work provides a new method in overcoming difficulty conduced by nonlinear stochastic perturbation.

Stochastic Perturbations of Fat Solenoidal Attractors

In this article stochastic perturbations of a class of fat solenoidal attractors are considered. We show the robustness of their invariant densities and rates of mixing under the stochastic perturbations by investigating the properties of their transfer operators.

Adaptive Stochastic Synchronization of Uncertain Delayed Neural Networks

This paper considers adaptive synchronization of uncertain neural networks with time delays and stochastic perturbation. A general adaptive controller is designed to deal with the difficulties deduced by uncertain parameters and stochastic perturbations, in which the controller is less conservative and optimal since its control gains can be automatically adjusted according to some designed update laws. Based on Lyapunov stability theory and Barbalat lemma, sufficient condition is obtained for synchronization of delayed neural networks by strict mathematical proof. Moreover, the obtained results of this paper are more general than most existing results of certainly neural networks with or without stochastic disturbances. Finally, numerical simulations are presented to substantiate our theoretical results.

Modeling of Stochastic Magnetic Perturbation by RWMEF-Coils on NSTX

A 3-D field line integration code, TRIP3D has been modified to model stochastic magnetic perturbation produced by a resistive wall mode, error field （ RWMEF ） coil in the NSTX tokamak with very low aspect ratio. The RWMEF-coil has two turns, which may produce stochastic fields with the toroidal mode number of n = 1 or 3. In this study, it is found that the stochastic field of n = 3 is larger than that of n=-1 for the same coil current. Two divertor discharges with lower single null （ LSN ） and double null （ DN ） configurations in the NSTX have been modeled with different RWMEF-coil currents and toroidal modes.

Stochastic optimal control for norovirus transmission dynamics by contaminated food and water

Norovirus is one of the most common causes of viral gastroenteritis in the world,causing significant morbidity,deaths,and medical costs.In this work,we look at stochastic modelling methodologies for norovirus transmission by water,human to human transmission and food.To begin,the proposed stochastic model is shown to have a single global positive solution.Second,we demonstrate adequate criteria for the existence of a unique ergodic stationary distribution R0 s>1 by developing a Lyapunov function.Thirdly,we find sufficient criteria Rs<1 for disease extinction.Finally,two simulation examples are used to exemplify the analytical results.We employed optimal control theory and examined stochastic control problems to regulate the spread of the disease using some external measures.Additional graphical solutions have been produced to further verify the acquired analytical results.This research could give a solid theoretical foundation for understanding chronic communicable diseases around the world.Our approach also focuses on offering a way of generating Lyapunov functions that can be utilized to investigate the stationary distribution of epidemic models with nonlinear stochastic disturbances.

Global impulsive exponential synchronization of stochastic perturbed chaotic delayed neural networks

In this paper, the global impulsive exponential synchronization problem of a class of chaotic delayed neural networks （DNNs） with stochastic perturbation is studied. Based on the Lyapunov stability theory, stochastic analysis approach and an efficient impulsive delay differential inequality, some new exponential synchronization criteria expressed in the form of the linear matrix inequality （LMI） are derived. The designed impulsive controller not only can globally exponentially stabilize the error dynamics in mean square, but also can control the exponential synchronization rate. Furthermore, to estimate the stable region of the synchronization error dynamics, a novel optimization control al- gorithm is proposed, which can deal with the minimum problem with two nonlinear terms coexisting in LMIs effectively. Simulation results finally demonstrate the effectiveness of the proposed method.

Joint state and parameter estimation in particle filtering and stochastic optimization

In this paper, an adaptive estimation algorithm is proposed for non-linear dynamic systems with unknown static parameters based on combination of particle filtering and Simultaneous Perturbation Stochastic Approxi- mation （SPSA） technique. The estimations of parameters are obtained by maximum-likelihood estimation and sampling within particle filtering framework, and the SPSA is used for stochastic optimization and to approximate the gradient of the cost function. The proposed algorithm achieves combined estimation of dynamic state and static parameters of nonlinear systems. Simulation result demonstrates the feasibilitv and efficiency of the proposed algorithm

Study of Heat Transport Across a Quasi-Stochastic Magnetic Field in Magnetic Confined Plasma Physics

Heat diffusion across a non-local quasi-stochastic magnetic field in tokamak plasma is numerically studied. The perturbed magnetic field is found to be a key factor in influencing effective radial heat conductivity whether the magnetic field is stochastic or not. Being different from previous work, a non-local perturbed magnetic field is used. Analytical results and numerical simulation results are compared between the conditions with a full and a quasi-perturbed stochastic field. The analytical results are found to be still consistent with numerical simulation results when the perturbed field is quasi-stochastic.

Persistence in a Stochastic SEIR Model with Constant Immigration in Incubation Period

A kind of stochastic susceptible-exposed but not infectiousinfectious-removed (SEIR) model with constant immigration in incubation period is presented, based on a deterministic SEIR model, via the technique of parameter perturbation which is standard in stochastic population modeling. The influence of the environmental noise as a standard Gaussian white noise on the epidemics' transmission is studied. Furthermore,the condition for the epidemics' persistence is obtained by formulating the corresponding function and using It 's formula. And the asymptotic behavior of the model near the endemic disease equilibrium is also studied. In this way, the decision support is provided in the application of this kind of stochastic SEIR model on the epidemics' prevention and control.

Extinction and persistence of a nonautonomous stochastic food-chain system with impulsive perturbations

In this paper, a nonautonomous stochastic food-chain system with functional response and impulsive perturbations is studied. By using Ito＇s formula, exponential martingale inequality, differential inequality and other mathematical skills, some sufficient conditions for the extinction, nonpersistence in the mean, persistence in the mean, and stochastic permanence of the system are established. Furthermore, some asymptotic properties of the solutions are also investigated. Finally, a series of numerical examples are presented to support the theoretical results, and effects of different intensities of white noises perturbations and impulsive effects are discussed by the simu｜ations.

Persistence and periodic measure of a stochastic predator-prey model with Beddington-DeAngelis functional response

In this paper,we study a stochastic predator-prey model with Beddington-DeAngelis functional response and time-periodic coefficients.By analyzing the stability of the solution on the boundary and some stochastic estimates,the threshold conditions for the time-average persistence in probability and extinction of each population are established.Furthermore,the existence of a unique periodic measure of the model is also presented under the condition of the time-average persistence in probability of the model.Several numerical simulations are given to verify the effectiveness of the theoretical results and to illustrate the effects of the white noises on the persistence and periodic measure of the model.

Stationary distribution and probability density function of a stochastic waterborne pathogen model with logistic growth

Waterborne disease threatens public health globally.Previous studies mainly consider that the birth of pathogens in water sources arises solely by the shedding of infected individuals,However,for free-living pathogens,intrinsic growth without the presence of hosts in environment could be possible.In this paper,a stochastic waterborne disease model with a logistic growth of pathogens is investigated.We obtain the sufficient conditions for the extinction of disease and also the existence and uniqueness of an ergodic stationary distribution if the threshold R_(0)^(s)>1.By solving the Fokker-Planck equation,an exact expression of probability density function near the quasi-endemic equilibrium is obtained.Results suggest that the intrinsic growth in bacteria population induces a large reproduction number to determine the disease dynamics.Finally,theoretical results are validated by numerical examples.

An Improved SPSA Algorithm for System Identification Using Fuzzy Rules for Training Neural Networks

Simultaneous perturbation stochastic approximation （SPSA） belongs to the class of gradient-free optimization methods that extract gradient information from successive objective function evaluation. This paper describes an improved SPSA algorithm, which entails fuzzy adaptive gain sequences, gradient smoothing, and a step rejection procedure to enhance convergence and stability. The proposed fuzzy adaptive simultaneous perturbation approximation （FASPA） algorithm is particularly well suited to problems involving a large number of parameters such as those encountered in nonlinear system identification using neural networks （NNs）. Accordingly, a multilayer perceptron （MLP） network with popular training algorithms was used to predicate the system response. We found that an MLP trained by FASPSA had the desired accuracy that was comparable to results obtained by traditional system identification algorithms. Simulation results for typical nonlinear systems demonstrate that the proposed NN architecture trained with FASPSA yields improved system identification as measured by reduced time of convergence and a smaller identification error.

A generalized stochastic competitive system with Ornstein-Uhlenbeck process

A generalized competitive system with stochastic perturbations is proposed in this paper,in which the stochastic disturbances are described by the famous Ornstein–Uhlenbeck process.By theories of stochastic differential equations,such as comparison theorem,Ito’s integration formula,Chebyshev’s inequality,martingale’s properties,etc.,the existence and the uniqueness of global positive solution of the system are obtained.Then sufficient conditions for the extinction of the species almost surely,persistence in the mean and the stochastic permanence for the system are derived,respectively.Finally,by a series of numerical examples,the feasibility and correctness of the theoretical analysis results are verified intuitively.Moreover,the effects of the intensity of the stochastic perturbations and the speed of the reverse in the Ornstein–Uhlenbeck process to the dynamical behavior of the system are also discussed.

Global stability of a stochastic predator-prey model with Allee effect

In this paper, we study a stochastic predator-prey model with Beddington-DeAngelis functional response and Allee effect, and show that there is a unique global positive solution to the system with the positive initial value. Sufficient conditions for global asymptotic stability are established. Some simulation figures are introduced to support the analytical findings.

QUALITATIVE ANALYSIS OF A STOCHASTIC PREDATOR-PREY SYSTEM WITH DISEASE IN THE PREDATOR

A stochastic predator prey system with disease in the predator population is proposed, the existence of global positive solution is derived. When the white noise is small, there is a stationary distribution. In addition, conditions of global stability for the determin- istic system are also established from the above result. By Lyapunov function, the long time behavior of solution around the disease-free equilibrium of deterministic system is derived. These results mean that stochastic system has the similar property with the corresponding deterministic system. When the white noise is small, however, large envi- ronmental noise makes the result different. Finally, numerical simulations are carried out to support our findings.

Synchronization-Based Topology Identification of Uncertain Stochastic Delay Complex Networks

In this paper, topology identification of general weighted complex network with time-varying delay and stochastic perturbation,which is a zero-mean real scalar Wiener process, is investigated. Based on the adaptive-feedback control method, the stochastic Lyapunov stability theory and the ito formula, some synchronous criteria are established, which guarantee the asymptotical mean square synchronization of the drive network and the response network with stochastic disturbances, as well as identify the topological structure of the uncertain general drive complex network. Finally, numerical simulations are presented to verify the correctness and effectiveness of the proposed scheme.

Stochastic modeling,analysis,and simulation of the COVID-19 pandemic with explicit behavioral changes in Bogota:Acase study

In this paper,a stochastic epidemiological model is presented as an extension of a compartmental SEIR model with random perturbations to analyze the dynamics of the COVID-19 pandemic in the city of Bogota D.C.,Colombia.This model incorporates thespread of COVID-19 impacted by social behaviors in the population and allows for projecting the number of infected,recovered,and deceased individuals considering the mitigation measures,namely confinement and partial relaxed restrictions.Also,the role of randomness using the concept of Brownian motion is emphasized to explain the behavior of the population.Computational experiments for the stochastic model with random perturbations were performed,and the model is validated through numerical simulations for actual data from Bogota D.C.