Intensity Of White Noise Research Articles

High robust eddy current tuned tandem mass dampers-inerters for structures under the ground acceleration

In this work, a novel eddy current tuned tandem mass dampers-inerters, referred to as EC-TTMDI is proposed, a theoretical analysis model of the vibration control mechanism is established, and parameterized analysis and design are conducted using the intelligent optimization algorithm. This model is the single-degree-of-freedom (SDOF) structure with EC-TTMDI subjected to Gaussian white noise base excitation. Specifically, the expression for the displacement variance of the SDOF structure-EC-TTMDI system was firstly obtained with resorting to both the equivalent linearization of eddy current damper (ECD) and residue theorem. The optimization objective function was then defined as minimization of the displacement variance, which is product of the white noise intensity and the square of H2 norm of the model transfer function. Employing the pattern-search algorithm, the variation trends of the objective function and the optimum design parameters were subsequently scrutinized. The vibration damping mechanism of EC-TTMDI is then revealed in terms of control effectiveness, robustness, structural frequency response, suppression bandwidth, and stroke. Finally, the time history response analysis of the SDOF structure-EC-TTMDI system subjected to the near-field impulse, near-field non-impulse, and far-field earthquakes was conducted to further confirm the performance superiority of EC-TTMDI. Results demonstrates that EC-TTMDI offers higher robustness and better control effectiveness compared to TTMDI and TMDI. Furthermore, EC-TTMDI features the damping force limiting characteristic, which enhances the integrity and reliability of TTMDI.

Stationary distribution of a stochastic generalized SIRI epidemic model with reinfection and relapse

In this paper, we propose and investigate the stochastic SIRI epidemic model with two generalized incidence rate functions. We firstly study the existence and uniqueness of the globally positive solution to the stochastic SIRI model with positive initial value. Then we obtain sufficient conditions for the extinction of the disease in the stochastic epidemic model, and find that the large noise can make the disease die out exponentially. Meanwhile, we obtain that the solution to the stochastic model has a unique stationary distribution when R0s˜ is greater than one. Our results show that the intensity of white noise can affect the dynamical behaviors of the model. Finally, we use numerical simulation to illustrate theoretical results, and apply both the stochastic and deterministic models to analyze the outbreak of COVID-19 epidemic in Serbia.

Dynamics of a Dengue Transmission Model with Multiple Stages and Fluctuations

A vector–host model of dengue with multiple stages and independent fluctuations is investigated in this paper. Firstly, the existence and uniqueness of the positive solution are shown by contradiction. When the death rates of aquatic mosquitoes, adult mosquitoes, and human beings respectively control the intensities of white noises, and if R0s>1, then the persistence in the mean for both infective mosquitoes and infective human beings is derived. When R0s>1 is valid, the existence of stationary distribution is derived through constructing several appropriate Lyapunov functions. If the intensities of white noises are controlled and φ<0 is valid, then the extinction for both infective mosquitoes and infective human beings is obtained by applying the comparison theorem and ergodic theorem. Further, the main findings are verified through numerical simulations by using the positive preserving truncated Euler–Maruyama method (PPTEM). Moreover, several numerical simulations on the infection scale of dengue in Fuzhou City were conducted using surveillance data. The main results indicate that the decrease in the transfer proportion from aquatic mosquitoes to adult mosquitoes reduces the infection scale of infective human beings with dengue virus, and the death rates of aquatic mosquitoes and adult mosquitoes affect the value of the critical threshold R0s. Further, the controls of the death rates of mosquitoes are the effective routes by the decision-makers of the Chinese mainland against the spread of dengue.

The diffusion behaviour of coupled particle rings driven by self-propelled particles in a two-dimensional reflection channel

Investigated the diffusion behavior of self-propelled coupled particle rings in a two-dimensional channel considering particle collisions. The channel geometry and noise regulation play crucial roles in directing transport within the system. Observed a significant alteration in the diffusion behavior of the particle rings at specific stages of the collision process, accompanied by corresponding changes in the diffusion coefficient. As the modulation phase shift increases, the mean square displacement (MSD) of the particle rings displays periodic fluctuations. The binding force between the particle rings partially restricts the growth of the MSD. An increase in white noise intensity enhances the diffusion behavior. The impact of self-propulsion speed is influenced by the modulation parameters. The sign of the modulation parameter dictates the correlation of the self-propulsion speed. Furthermore, the number of particle rings in the channel introduces a complex effect on the diffusion behavior.

Deterministic vs. stochastic dynamics of a predator–prey system with disease in prey: Impact of fear and supplementary foods

In this study, we delve into the dynamics of a generalist predator–prey system with prevalence of a disease in the prey population and the presence of predator-induced fear. In this intricate ecological web, the fear response triggered by predators influences the birth rate of susceptible prey population and also escalates intra-specific competition among them. In an effort to encapsulate a more realistic scenario, we extend our deterministic model to its stochastic counterpart by introducing environmental white noise that impacts the mortality rates of both prey and predator species. Comprehensive mathematical analyses are performed on both the deterministic and stochastic systems to elucidate their qualitative behaviors. Specifically, we derive conditions under which the stochastic system exhibits a unique global positive solution and explore the potential extinction of species within the ecosystem. To unravel the intricate dynamics numerically, we perform sensitivity of parameters, and construct one- and two-parameter bifurcation diagrams. Our investigations reveal that when the costs of fear surpass specific thresholds and disease incidence is high, both the susceptible and infected prey populations face extinction. Notably, the introduction of supplementary foods can lead to system’s destabilization, potentially pushing it towards a state where only predators can persist. Moreover, we observe that lower intensities of white noise have minimal impact on the system’s dynamics, while higher noise intensities introduce substantial fluctuations and may precipitate the extinction of species within the ecosystem. Furthermore, we elucidate the abundances of prey and predator species within the ecosystem through histogram plots.

Correlated non-Gaussian and Gaussian noises induced transition and mean first-passage time in a fractional-order bistable system

The transition and mean first-passage time(MFPT) in a fractional-order bistable system, excited by multiplicative non-Gaussian noise and additive Gaussian white noise, are investigated. Utilizing the fractional-order minimum mean square error criterion and the path integral approach, we derive approximate expressions for both the steady-state probability distribution function and the MFPT. The results show that the noise correlation strength, non-Gaussian parameter, Gaussian noise strength and fractional order can induce phase transitions. The MFPT exhibits a peak as a function of non-Gaussian noise intensity, demonstrating the noise-enhanced stability phenomenon, while the MFPT displays a consistent, monotonic relationship as a function of Gaussian white noise intensity. Numerical simulations are conducted to validate theoretical results, which show a reasonably high degree of consistency.

Morphosyntactic agreement in English: does it help the listener in noise?

English morphosyntactic agreement, such as determiner–noun agreement in These cabs broke down and noun–verb agreement in The cabs break down, has a few interesting properties that enable us to investigate whether agreement has a psycholinguistic function, that is, whether it helps the listener process linguistic information expressed by a speaker. The present project relies on these properties in a perception experiment, examines the two aforementioned types of English agreement, and aims at analyzing whether and how native English listeners benefit from agreement. The two types of agreement were contrasted with cases without any overtly agreeing elements (e.g. The cabs broke down). Native speakers of English with normal hearing heard short English sentences in quiet and in more or less intense white noise and were requested to indicate whether the second word of the sentence (e.g. These cabs broke down) was a singular or plural noun. Accuracy was entered as the response variable in the binomial logistic regression model. Results showed that overt determiner–noun agreement clearly increased response accuracy, while noun–verb agreement had at best marginal effects. The findings are interpreted against the background of functional aspects of linguistic structures in English, in the context of unfavorable listening conditions in particular.

Stochastic evolutionary game analysis of tacit knowledge sharing in patent commercialization

AbstractGiven the rapid prevalence and advancement of patent commercialization, tacit knowledge sharing during this process is increasingly being scrutinized. To explore the factors affecting tacit knowledge sharing in patent commercialization, this paper constructed a tripartite stochastic evolutionary game model to analyze the complex game interaction between inventors, enterprises, and patent intermediaries. Due to uncertainty in the external environment, Gaussian white noise was introduced into replicator dynamic equations, and numerical simulation was used to describe the tripartite dynamic evolution. The results showed the following: (1) inventors and enterprises with similar levels of relevant capabilities are more likely to achieve better results in sharing tacit knowledge. (2) The implementation of an effective market reputation evaluation system has the potential to enhance implicit knowledge sharing in the realm of patent commercialization. (3) The percentage of payments of the two‐stage payment contract will affect the behavior of inventors and enterprises. (4) The stability of the equilibrium solution is closely tied to the intensity of Gaussian white noise, which can lead to deviations from the original trajectory of equilibrium strategies. Greater external uncertainty makes tacit knowledge sharing more challenging. This study will provide constructive suggestions for promoting tacit knowledge sharing among participants in patent commercialization.

Dynamics of a generalist predator–prey system with harvesting and hunting cooperation in deterministic/stochastic environment

In this investigation, we explore a predator–prey system characterized by generalist predators exhibiting cooperative behavior during hunting, subject to nonlinear harvesting rate. Employing a Beverton–Holt type functional response to capture the impact of additional food sources on predator growth, our numerical findings affirm the destabilizing influence of hunting cooperation, excessive predation, and supplementary food sources. Conversely, the system demonstrates stabilization in response to increased prey species growth. We unveil the occurrence of both forward and backward bifurcations in the system due to the predator growth attributed to additional food sources, contingent on the degree of hunting cooperation. To broaden the scope, we extend our proposed model to its stochastic counterpart, introducing environmental white noises. Our numerical results anticipate that higher intensities of white noises lead to fluctuations of greater amplitude, while smaller intensities exhibit a more modest impact. Additionally, we elucidate the dynamics of prey and predator populations through histogram plots. The theoretical and numerical insights derived from this study provide a deeper understanding of the intricate dynamics within predator–prey systems of ecological communities, emphasizing the significance of additional food sources for cooperative predators subject to harvesting in both constant and fluctuating environments.

New Results on the Asymptotic Behaviour of a Stochastic SEI Model of Lymphatic Filariasis

The goal of this article is to examine a new stochastic epidemic model for lymphatic filariasis, susceptible‐exposed‐infected (SEI). Like other diseases, the spread of lymphatic filariasis is subject to a degree of randomness due to fluctuations in the natural environment. This provides us with the opportunity to formulate a mathematical model of lymphatic filariasis that comprehensively considers external stochastic influences. By using carefully designed stochastic Lyapunov functions, we establish sufficient conditions for the eradication of lymphatic filariasis infections. Moreover, under specific conditions regarding the intensity of white noise, we also demonstrate the existence of a unique ergodic stationary distribution and the persistence of the mean for the model. Numerical simulations are conducted to substantiate the validity of our findings.

Stochastic and Deterministic Models for Rubella Dynamics with Two Doses of Vaccination and Vertical Transmission

Rubella is a highly contagious viral disease that can be transmitted through contact with infected people or objects. If a pregnant woman is infected with rubella, the virus can be transmitted to the fetus, which can cause birth defects. To prevent rubella, children need to receive the MMR vaccine twice. In this study, we developed a deterministic and stochastic mathematical model to investigate the dynamics of rubella infection, considering vertical transmission and environmental factors. The model divides the population into five groups: susceptible, first vaccinated, protected, infected, and recovered. From the perspective of the qualitative behavior of the model, the model is bound to an invariant domain, and all solutions within the compartment are positive. We analyzed the equilibrium point of the model and its stability, and we determined the basic reproductive number using the next‐generation matrix. The basic reproductive number for the stochastic model is smaller than that for the deterministic model due to randomness. By comparing the two models in terms of the basic reproductive number, extending the deterministic model to a stochastic model can provide more realistic information about the disease, predict its dynamic propagation, and give suggestions for control mechanisms. Numerical simulations and sensitivity analyses were performed to study the influence of fundamental parameters, and the simulation results were displayed graphically using the MATLAB computer software. Parameter values were obtained from published papers, some of which were assumed. The simulation results show that the stochastic curve is not as smooth as the deterministic curve due to the randomness of the rubella. The consideration of the double vaccination dose and white noise intensity plays an important role in predicting disease status and minimizing and eradicating rubella. Therefore, reducing vertical infection and transmission rates and increasing vaccination and recovery rates will help to prevent and control the spread of rubella.

A delayed deterministic and stochastic [formula omitted] model: Hopf bifurcation and stochastic analysis

In this paper, we present a delayed deterministic and stochastic SIRICV models to investigate the effects of the white noise intensities and the waning immunity of vaccinated individuals in the evolution of the disease. For the deterministic SIRICV model, the basic reproduction number R0 and the equilibrium points are calculated. The local stability of equilibrium points is analyzed. Particularly, when R0<1 the disease-free equilibrium is locally stable for any positive value of τ. Furthermore, when R0>1, the local stability and sufficient conditions to ensure the occurrence of Hopf bifurcation for the endemic equilibrium point are established by considering the time delay τ as a bifurcation parameter. For the stochastic SIRICV model, the conditions of the extinction and persistence of the disease are given by using the stochastic basic reproduction numbers R0s and R0s∗. Numerical simulations are presented to enhance our analytical results and contrast the deterministic and stochastic models.

STOCHASTIC PERMANENCE AND EXTINCTION OF AN EPIDEMIC MODEL WITH SATURATED TREATMENT

We propose and study the transmission dynamics of susceptible-exposed-infected-recovered [Formula: see text] epidemic model with saturated treatment function. We consider saturated treatment function in the epidemic system to understand the effect of delayed treatment on the disease transmission. The indiscriminately perturbation which is considered as a type of white noise is proportional to the distance of state variables from the values of endemic equilibria. Choosing the suitable Lyapunov function and using the It[Formula: see text]’s formula, the existence and the uniqueness of the positive solution of the system are examined. Stochastic boundedness, permanence and extinction of the epidemic model are investigated with proper conditions. Numerical simulations are performed to illustrate our results. The sensitivity analysis of the basic reproduction number is performed. The effect of control parameter is determined on the model dynamics. It is our main finding that the different intensities of white noises can fluctuate the susceptible, exposed, infected, recovered individuals around its equilibrium points.

Stochastic solitons in a two-layer fluid system

In this paper, stochastic one- and two-soliton solutions for the stochastic Benjamin–Ono equation modeling the nonlinear random waves in a two-layer fluid system with and without the uneven bottom topography are derived via the Gaussian white noise functional approach and the Hirota method. The effects of Gaussian white noise on the propagation and the interaction of the stochastic solitons are discussed. In the stochastic-one-soliton case, impact on the velocity is enlarged with the increase of the intensity of Gaussian white noise while the soliton amplitude and shape keep unchanged during the propagation. We also investigate the results of the stochastic-two-soliton interaction and the effects of Gaussian white noise on the interaction of stochastic two solitons. With the increase of Gaussian white noise, the velocity of two solitons causes the corresponding change, while the soliton amplitudes and shapes keep unchanged before and after the interaction. • Successfuly obtaining the stochastic one-soliton, two-soliton and N-soliton solutions of the stochastic Benjamin–Ono equation. • Investigating the effect of Gaussian white noise on propagation and interactions of the stochastic solitons. • The impact on the velocity can be greater as the intensity of Gaussian white noise increases in the stochastic one-soliton case. • The amplitude keep unchange along the propagation in the stochastic one-soliton case. • There is a change over the velocities of the stochastic two solitons when there exists white noise.

Modeling and analysis of a stochastic giving-up-smoking model with quit smoking duration.

Smoking has gradually become a very common behavior, and the related situation in different groups also presents different forms. Due to the differences of individual smoking cessation time and the interference of environmental factors in the spread of smoking behavior, we establish a stochastic giving up smoking model with quit-smoking duration. We also consider the saturated incidence rate. The total population is composed of potential smokers, smokers, quitters and removed. By using Itô's formula and constructing appropriate Lyapunov functions, we first ensure the existence of a unique global positive solution of the stochastic model. In addition, a threshold condition for extinction and permanence of smoking behavior is deduced. If the intensity of white noise is small, and $ \widetilde{\mathcal{R}}_0 < 1 $, smokers will eventually become extinct. If $ \widetilde{\mathcal{R}}_0 > 1 $, smoking will last. Then, the sufficient condition for the existence of a unique stationary distribution of the smoking phenomenon is studied as $ R_0^s > 1 $. Finally, conclusions are explained by numerical simulations.

Искусственный интеллект для контроля передачи данных в тактическом звене управления с использованием многослойного и многопотокового шифрования геопространственной обстановки

The paper presents the development of a scientific and technical solutions to control data trans-mission set. In particular, the using cryptographic multilayer encryption algorithms possibility is considered. Algorithms can display the geospatial terrain situation. Multithreaded computational programs allowing to mask geospatial environment with various white noise intensity were created.

Feedback stabilization of quasi nonintegrable Hamiltonian systems under combined Gaussian and Poisson white noise excitations

A procedure for designing a feedback control to asymptotic Lyapunov stability with probability one of quasi nonintegrable Hamiltonian systems under combined Gaussian and Poisson white noise excitations is proposed. First, a one dimensional partially averaged Itô stochastic differential equation for controlled Hamiltonian is derived from the motion equations of the system by using the stochastic averaging method. Second, the dynamical programming equation for the ergodic control problem of the averaged system with undetermined cost function is set up based on the dynamical programming principle and the jump–diffusion chain stochastic differential rules. The optimal control law is obtained by solving the dynamical programming equation. Third, the analytical expression for the largest Lyapunov exponent of the averaged system is derived. Finally, the asymptotic Lyapunov stability with probability one of the originally controlled system is analyzed approximately by using the largest Lyapunov exponent. The cost function and optimal control forces are determined by the requirements of stabilizing the system. An example is worked out in detail to illustrate the effectiveness of the proposed method for stabilization control, and the control effect of the proposed feedback stabilization varies with the change of parameters is also studied in this paper, such as, the greater the excitation intensity of Gaussian and Poisson white noise, the better the stabilization control effect.

Harvesting of a Stochastic Population Under a Mixed Regular-Singular Control Formulation

This work focuses on optimal harvesting-renewing for a stochastic population. A mixed regular-singular control formulation with a state constraint and regime switching is introduced. The decision-makers either harvest or renew with finite or infinite harvesting/renewing rates. The payoff functions depend on the harvesting/renewing rates. Several properties of the value function are established. The limiting value function as the white noise intensity approaches infinity is identified. The Markov chain approximation method is used to find numerical approximation of the value function and optimal strategies.

A stochastically perturbed co-infection epidemic model for COVID-19 and hepatitis B virus.

A new co-infection model for the transmission dynamics of two virus hepatitis B (HBV) and coronavirus (COVID-19) is formulated to study the effect of white noise intensities. First, we present the model equilibria and basic reproduction number. The local stability of the equilibria points is proved. Moreover, the proposed stochastic model has been investigated for a non-negative solution and positively invariant region. With the help of Lyapunov function, analysis was performed and conditions for extinction and persistence of the disease based on the stochastic co-infection model were derived. Particularly, we discuss the dynamics of the stochastic model around the disease-free state. Similarly, we obtain the conditions that fluctuate at the disease endemic state holds if min (mathbf {R}_{H}^s,mathbf {R}_{C}^s,mathbf {R}_{HC}^s)> 1. Based on extinction as well as persistence some conditions are established in form of expression containing white noise intensities as well as model parameters. The numerical results have also been used to illustrate our analytical results.

Dynamics of a Stochastic HIV Infection Model with Logistic Growth and CTLs Immune Response under Regime Switching

Considering the influences of uncertain factors on the reproduction of virus in vivo, a stochastic HIV model with CTLs’ immune response and logistic growth was developed to research the dynamics of HIV, where uncertain factors are white noise and telegraph noise. which are described by Brownian motion and Markovian switching, respectively. We show, firstly, the existence of global positive solutions of this model. Further, by constructing suitable stochastic Lyapunov functions with regime switching, some sufficient conditions for the existence and uniqueness of the stationary distribution and the conditions for extinction are obtained. Finally, the main results are explained by some numerical examples. Theoretical analysis and numerical simulation show that low-intensity white noise can maintain the persistence of the virus, and high intensity white noise can make the virus extinct after a period of time with multi-states.