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Fluctuations are inherent to biological systems, arising from the stochastic nature of molecular interactions, and influence various aspects of system behavior, stability, and robustness. These fluctuations can be categorized as intrinsic, stemming from the system's inherent structure and dynamics, and extrinsic, arising from external factors, such as temperature variations. Understanding the interplay between these fluctuations is crucial for obtaining a comprehensive understanding of biological phenomena. However, studying these effects poses significant computational challenges. In this study, we used an underexplored methodology to analyze the effect of extrinsic fluctuations in stochastic systems using ordinary differential equations instead of solving the master equation with stochastic parameters. By incorporating temperature fluctuations into reaction rates, we explored the impact of extrinsic factors on system dynamics. We constructed a master equation and calculated the equations for the dynamics of the first two moments, offering computational efficiency compared with directly solving the chemical master equation. We applied this approach to analyze a biological oscillator, focusing on the p53 model and its response to temperature-induced extrinsic fluctuations. Our findings underscore the impact of extrinsic fluctuations on the nature of oscillations in biological systems, with alterations in oscillatory behavior depending on the characteristics of extrinsic fluctuations. We observed an increased oscillation amplitude and frequency of the p53 concentration cycle. This study provides valuable insights into the effects of extrinsic fluctuations on biological oscillations and highlights the importance of considering them in more complex systems to prevent unwanted scenarios related to health issues. [ABSTRACT FROM AUTHOR]

In the study of stochastic systems, the committor function describes the probability that a system starting from an initial configuration x will reach a set B before a set A. This paper introduces an efficient and interpretable algorithm for approximating the committor, called the "fast committor machine" (FCM). The FCM uses simulated trajectory data to build a kernel-based model of the committor. The kernel function is constructed to emphasize low-dimensional subspaces that optimally describe the A to B transitions. The coefficients in the kernel model are determined using randomized linear algebra, leading to a runtime that scales linearly with the number of data points. In numerical experiments involving a triple-well potential and alanine dipeptide, the FCM yields higher accuracy and trains more quickly than a neural network with the same number of parameters. The FCM is also more interpretable than the neural net. [ABSTRACT FROM AUTHOR]

The time-periodic modulation of a temperature gradient can alter the heat transport properties of a physical system. Oscillating thermal gradients give rise to behaviors such as modified thermal conductivity and controllable time-delayed energy storage that are not present in a system with static temperatures. Here, we examine how the heat transport properties of a molecular lattice model are affected by an oscillating temperature gradient. We use analytical analysis and molecular dynamics simulations to investigate the vibrational heat flow in a molecular lattice system consisting of a chain of particles connected to two heat baths at different temperatures, where the temperature difference between baths is oscillating in time. We derive expressions for heat currents in this system using a stochastic energetics framework and a nonequilibrium Green's function approach that is modified to treat the nonstationary average energy fluxes. We find that emergent energy storage, energy release, and thermal conductance mechanisms induced by the temperature oscillations can be controlled by varying the frequency, waveform, and amplitude of the oscillating gradient. The developed theoretical approach provides a general framework to describe how vibrational heat transmission through a molecular lattice is affected by temperature gradient oscillations. [ABSTRACT FROM AUTHOR]

The ability to distinguish between stochastic systems based on their trajectories is crucial in thermodynamics, chemistry, and biophysics. The Kullback–Leibler (KL) divergence, D KL A B (0 , τ) , quantifies the distinguishability between the two ensembles of length-τ trajectories from Markov processes A and B. However, evaluating D KL A B (0 , τ) from histograms of trajectories faces sufficient sampling difficulties, and no theory explicitly reveals what dynamical features contribute to the distinguishability. This work provides a general formula that decomposes D KL A B (0 , τ) in space and time for any Markov processes, arbitrarily far from equilibrium or steady state. It circumvents the sampling difficulty of evaluating D KL A B (0 , τ). Furthermore, it explicitly connects trajectory KL divergence with individual transition events and their waiting time statistics. The results provide insights into understanding distinguishability between Markov processes, leading to new theoretical frameworks for designing biological sensors and optimizing signal transduction. [ABSTRACT FROM AUTHOR]

Order release optimisation is essential in production planning, especially in discrete manufacturing. Order release planning models with load-dependent lead times must anticipate the time-dependent work-in-process and output for any given release schedule and thus require an anticipation model that approximates the time-dependent behaviour of queueing systems. We present a generic optimisation model for order release planning in stochastic, non-stationary manufacturing systems that includes a well-defined interface for the anticipation model. We develop two stationary backlog carryover (SBC) approaches to approximate time-dependent queueing behaviour and prove their consistency with the order release model. The resulting nonlinear programming model is shown to be a special case of the well-known clearing function models. A numerical study demonstrates that the optimised order releases for different demand patterns are close to the optimum that results from simulation-based optimisation even for extreme demand and release patterns. The resulting output closely matches the simulated output with some deviations. [ABSTRACT FROM AUTHOR]

The current challenge faced by the global research community is how to effectively address, manage, and control the spread of infectious diseases. This research focuses on conducting a dynamic system analysis of a stochastic epidemic model capable of predicting the persistence or extinction of the dengue disease. Numerical methodology on deterministic procedures, i.e. Adams method and stochastic/probabilistic schemes, i.e. stochastic Runge–Kutta method, is employed to simulate and forecast the spread of disease. This study specifically employs two nonlinear mathematical systems, namely the deterministic vector-borne dengue epidemic (DVBDE) and the stochastic vector-borne dengue epidemic (SVBDE) models, for numerical treatment. The objective is to simulate the dynamics of these models and ascertain their dynamic behavior. The VBDE model segmented the population into the following five classes: susceptible population, infected population, recovered population, susceptible mosquitoes, and the infected mosquitoes. The approximate solution for the dynamic evolution for each population is calculated by generating a significant number of scenarios varying the infected population's recovery rate, human population birth rate, mosquitoes birth rate, contaminated people coming into contact with healthy people, the mortality rate of people, mosquitos population death rate and infected mosquito contact rate with population that is not infected. Comparative evaluations of the deterministic and stochastic models are presented, highlighting their unique characteristics and performance, through the execution of numerical simulations and analysis of the results. [ABSTRACT FROM AUTHOR]

This study discusses consensus tracking control problems for nonlinear stochastic multi‐agent systems under DoS attacks and deception attacks. The above attacks are respectively described as receiving duplicate data and receiving false data. In an effort to save network resources, this study proposes an appropriate dynamic event‐triggered mechanism. On this basis, a feedback controller for consensus tracking is designed. Then, a new consensus tracking criterion under dual network attacks is proposed. In addition, by selecting a new Lyapunov–Krasovskii functional and using Jesen inequality, sufficient conditions for system mean‐square stability are obtained. Finally, the efficacy of this approach is validated through a numerical example. [ABSTRACT FROM AUTHOR]

This article discusses the finite‐time boundedness (FTB) issue and L2$$ {L}_2 $$‐gain analysis for switched stochastic systems, particularly under the dual influence of DoS attacks and false data injection attacks, by employing a novel event‐triggered mechanism. Different from the moment calculation method, a probability‐based FTB is studied which offers more pertinence. To obtain a less conservative condition of FTB, a switched Lyapunov function is constructed. Additionally, a memory‐based dynamic event‐triggered mechanism is designed to reduce the amounts of triggering and mitigate the state response fluctuations. Based on the incomplete information above, state feedback controllers are devised to satisfy stochastic FTB, ensuring the successful attainment of finite‐time L2$$ {L}_2 $$‐gain. Sufficient conditions are cast into a convex optimization problem by LMIs which can be solved easily. Finally, a compared numerical example and an RLC series circuit are adopted to demonstrate the availability of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is devoted to proving the small noise asymptotic behavior, particularly large deviation principle, for multi-scale stochastic dynamical systems with fully local monotone coefficients driven by multiplicative noise. The main techniques rely on the weak convergence approach, the theory of pseudo-monotone operators and the time discretization scheme. The main results derived in this paper have broad applications to various multi-scale models, where the slow component could be such as stochastic porous medium equations, stochastic Cahn-Hilliard equations and stochastic 2D Liquid crystal equations. [ABSTRACT FROM AUTHOR]

In this paper, we consider the dynamics of integrable stochastic Hamiltonian systems. Utilizing the Nagaev-Guivarc'h method, we obtain several generalized results of the central limit theorem. Making use of this technique and the Birkhoff ergodic theorem, we prove that the invariant tori persist under stochastic perturbations. Moreover, they asymptotically follow a Gaussian distribution, which gives a positive answer to the stability of integrable stochastic Hamiltonian systems over time. Our results hold true for both Gaussian and non-Gaussian noises, and their intensities can be not small. [ABSTRACT FROM AUTHOR]

Real-time forecasting of infectious diseases is crucial for effective public health management, particularly during outbreaks. When infectious disease predictions are based on mechanistic models, they can guide resource allocation and help evaluate the potential effects of different interventions. However, accurately parametrizing these models in real time presents a challenge, as timely information on behavioral shifts, interventions and transmission pathways is often lacking. This investigation leverages the artificial neural networks with the Bayesian regularization (BR-ANN) backpropagation approach to examine the dynamical pathogen spread with Wiener process incorporation. The stochastic differential model is structured into susceptible, vaccinated, infectious and susceptible (SVIS) compartments. The Kloeden–Platen–Schurz (KPS) computing paradigm for the stochastic differential system is utilized to generate synthetic datasets by applying transformations to key factors, including the population recruitment ratio, transmission ratio of vulnerable individuals, natural death rate of the population, vaccination rate of vulnerable individuals, total population size, immune loss ratio of susceptible individuals, recovery rate and mortality rate from the disease among infected individuals. Random selection from the generated datasets is exploited for the training and testing procedures for constructing the BR-ANN networks. The significance of the proposed scheme for various stochastic SVIS system scenarios is endorsed by the comprehensive assessments of the BR-ANN approach that are conducted by means of extensive experimentations and comparison with the reference KPS solutions of the SVIS system in terms of MSE optimal performance plots, absolute errors, autocorrelation analysis, regression indices and error histograms. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a continuous-time linear quadratic stochastic optimal control (LQSOC) problem in an infinite horizon, where diffusion and drift terms of the corresponding stochastic system depend on both state and control variables. In light of the stochastic control theory, this LQSOC problem is reduced to solving a generalised algebraic Riccati equation (GARE). With the help of an existing model-based value iteration (VI) algorithm, we propose two data-driven VI algorithms to solve the GARE. The first one relies on transforming the stochastic system into a deterministic control system first and then solving the LQSOC problem by the data of the deterministic system. Consequently, this algorithm does not need the information of two system coefficients and has a lower algorithm complexity. The second algorithm directly uses the data generated by the stochastic system, and thus it circumvents the requirement of all system coefficients. We also provide convergence proofs of these two data-driven algorithms and validate these algorithms through two simulation examples. [ABSTRACT FROM AUTHOR]

In this study, we examine whether mild solutions to a fractional stochastic evolution system with a fractional Caputo derivative on an infinite interval exist and are attractive. We use semigroup theory, fractional calculus, stochastic analysis, compactness methods, and the measure of noncompactness (MNC) as the foundation for our methodologies. There are several suggested sufficient requirements for the existence of mild solutions to the stated problem. Examples that highlight the key findings are provided. [ABSTRACT FROM AUTHOR]

This paper addresses the existence and exponential stability problem of highly nonlinear hybrid neutral pantograph stochastic equations with multiple delays (HNPSDEswMD). By Lyapunov functional method and without laying down a linear growth condition, the above problem of the exact solution is shown. We end up with two numerical examples that corroborates our theoretical findings. [ABSTRACT FROM AUTHOR]

Abstract.We investigate the long-time behavior of 2D stochastic electrokinetic flow modeled by the stochastic Nernst-Planck-Navier-Stokes system with a blocking boundary for ionic species concentrations in a smooth bounded domain 풟. The existence of invariant measure is established for the multiplicative noise case corresponding to two situations: two opposite charged ionic species, multiple species with equal diffusivity and same magnitude for all valences. When the noise is additive case, our findings demonstrate that the invariant measure exhibits the ergodicity and exponentially mixing. This conclusion is based on the result of exponentially stability analysis. [ABSTRACT FROM AUTHOR]

In this article, the adaptive fixed‐time prescribed performance (FTPP) regulation is investigated for a class of time‐varying state constrained switched stochastic systems with input delay. The time‐varying barrier Lyapunov function and a compensation system are presented, respectively, to deal with the design problems caused by the existence of both time‐varying state constraints and input delay. Some radial basis function neural networks are used to approximate unknown functions, and the common Lyapunov function method is displayed to handle the switched signals. Besides, by designing a fixed‐time prescribed performance function, the desired adaptive neural controller is constructed. Compared with the existing works for state constrained control problem, the FTPP regulation control scheme is first proposed for time‐varying state constrained stochastic switched systems under input delay, and the adaptive dynamic surface control scheme with the nonlinear filter is designed to solve the problem of "explosion of complexity." Based on the stochastic stability theory, the FTPP of system output is achieved, other system state variables are restricted in the predefined regions, and all signals of this closed‐loop system remain bounded in probability. Finally, the availability of the proposed control scheme is illustrated via two simulation examples. [ABSTRACT FROM AUTHOR]

The impact of an external noise signal on a memristor is studied. Under Gaussian white noise, the memristor switches randomly between the high resistance state and the low resistance one in the random telegraph signal (RTS) mode. Such a behavior is typical for the stochastic bistable systems. The power spectral density of the electric current flowing through the memristor switching in the RTS mode manifested series of equally spaced drops at the Kramers rates of the RTS process and their higher harmonics against the background of the f−2 Lorentz decay. This result indicates the memristor to absorb the noise signal energy not uniformly (over the entire broadband noise spectrum) but resonantly, at specific frequencies inherent to the memristor itself. The experimental results are interpreted on the base of the model of Brownian particle motion in a bistable potential. The results of this study demonstrate the fundamental properties of the memristor as a stochastic multistable system. [ABSTRACT FROM AUTHOR]

ABSTRACT This paper proposes a novel event‐triggered adaptive asymptotic tracking control (ATC) method for stochastic non‐linear systems with unknown hysteresis. Firstly, in order to reduce the depletion of network resources while optimizing the asymptotic tracking performance of the system, a switching threshold mechanism (STM)‐based event‐triggered control (ETC) strategy is adopted. Secondly, a first‐order filter is utilized to address the problem of the contradiction between event‐triggered mechanism (ETM) output and rate‐dependent hysteresis actuator input. By incorporating an enhanced backstepping technique and a bounded estimation method, it is rigorously demonstrate that the system achieves zero tracking error, effectively compensates for unknown hysteresis, and ensures that all closed‐loop signals remain bounded in probability. Meanwhile, the Zeno phenomenon is excluded. Finally, the effectiveness and superiority of the proposed control scheme are verified by the simulation results. [ABSTRACT FROM AUTHOR]

This paper considers the Keller-Segel model coupled to stochastic Navier-Stokes equations (KS-SNS, for short), which describes the dynamics of oxygen and bacteria densities evolving within a stochastically forced 2D incompressible viscous flow. Our main goal is to investigate the existence and uniqueness of global solutions (strong in the probabilistic sense and weak in the PDE sense) to the KS-SNS system. A novel approximate KS-SNS system with proper regularization and cut-off operators in H s (R 2) is introduced, and the existence of approximate solution is proved by some a priori uniform bounds and a careful analysis on the approximation scheme. Under appropriate assumptions, two types of stochastic entropy-energy inequalities that seem to be new in their forms are derived, which together with the Prohorov theorem and Jakubowski-Skorokhod theorem enables us to show that the sequence of approximate solutions converges to a global martingale weak solution. In addition, when χ (⋅) ≡ const. > 0 , we prove that the solution is pathwise unique, and hence by the Yamada-Wantanabe theorem that the KS-SNS system admits a unique global pathwise weak solution. [ABSTRACT FROM AUTHOR]

We study the dynamics of waves, oscillations, and other spatio-temporal patterns in stochastic evolution systems, including SPDE and stochastic integral equations. Representing a given pattern as a smooth, stable invariant manifold of the deterministic dynamics, we reduce the stochastic dynamics to a finite dimensional SDE on this manifold using the isochronal phase. The isochronal phase is defined by mapping a neighborhood of the manifold onto the manifold itself, analogous to the isochronal phase defined for finite-dimensional oscillators by A.T. Winfree and J. Guckenheimer. We then determine a probability measure that indicates the average position of the stochastic perturbation of the pattern/wave as it wanders over the manifold. It is proved that this probability measure is accurate on time-scales greater than O (σ − 2) , but less than O (exp ⁡ (C σ − 2)) , where σ ≪ 1 is the amplitude of the stochastic perturbation. Moreover, using this measure, we determine the expected velocity of the difference between the deterministic and stochastic motion on the manifold. [ABSTRACT FROM AUTHOR]

The paper focuses on the study of an epidemic model for the evolution of diseases, using stochastic models. We demonstrated the encoding of this intricate model into formalisms suitable for analysis with advanced stochastic model checkers. A co-infection model's dynamics were modeled as an Ito–Levy stochastic differential equations system, representing a compartmental system shaped by disease complexity. Initially, we established a deterministic system based on presumptions and disease-related traits. Through non-traditional analytical methods, two key asymptotic properties: eradication and continuation in the mean were demonstrated. Section 2 provides a detailed construction of the model. Section 3 results confirm that the outcome is biologically well-behaved. Utilizing simulations, we tested and confirmed the stability of all equilibrium points. The ergodic stationary distribution and extinction conditions of the system are thoroughly analyzed. Investigations were made into the stochastic system's probability density function, and digital simulations were employed to illustrate the probability density function and systems' extinction. Although infectious disease control and eradication are major public health goals, global eradication proves challenging. Local disease extinction is possible, but it may reoccur. Extinction is more feasible with a lower . Notably, our simulations showed that reducing the value significantly increases the likelihood of disease extinction and reduces the probability of future recurrence. Additionally, our study provides insights into the conditions under which a disease can persist or become extinct, contributing to more effective disease control strategies in public health. [ABSTRACT FROM AUTHOR]

In this article, the issue of adaptive fuzzy finite‐time command filtered control is discussed for nonlinear stochastic systems subject to unknown dead‐zone constraints and unmodeled dynamics. The packaged unknown nonlinearities are approximated by introducing fuzzy logic systems. An improved technique is introduced to cope with unknown functions with the structure of nonstrict‐feedback in the operation of controller design. Under the criterion of finite‐time stability, a novel fast convergent control scheme is developed. Additionally, the effect of filter errors bought by the command filters is diminished via applying corresponding error compensating signals and a measurable dynamic signal is adopted to handle unmodeled dynamics. The improved designed controller not only guarantees all the closed‐loop signals remain finite‐time bounded, but also makes the system output follows the given desirable trajectory under the bounded error. The usefulness of the designed strategy can be verified through the numerical and practical examples. [ABSTRACT FROM AUTHOR]

This paper aims to investigate a new class of fractional stochastic differential systems under the influence of damping and Poisson jumps. First, the existence and uniqueness of mild solutions for the proposed system are investigated under the non-Lipschitz conditions. The results are formulated and proved by using the $ (\beta,\delta) $ (β , δ) -regularised family, Grönwall's inequality, and successive approximation technique, which is different from the fixed point approach. Moreover, novel stability criteria for the considered system are obtained by utilising the corollary of the Bihari inequality. Finally, the correctness of the obtained results is verified by example. [ABSTRACT FROM AUTHOR]

We establish that, under certain conditions, the set of random occupational measures generated by the state-control trajectories of a discrete-time stochastic system as well as the set of their mathematical expectations converge to a non-random, convex and compact set. We apply these results to the averaging a hybrid system with a slow continuous-time component and a fast discrete-time component. It is shown that the solutions of the hybrid system are approximated by the solutions of a differential inclusion. The novelty of our results is that we allow the state-control space of the fast component to be non-denumerable. [ABSTRACT FROM AUTHOR]

The Pareto optimality of stochastic cooperative differential game with a discrete delay, a moving-average delay and a noisy memory process is studied. We establish two sets of equivalent necessary and sufficient conditions for Pareto efficient strategies. The first set comes from reduction to a discrete delayed Pareto optimality, while the second set given by Malliavin derivative is derived by the decomposition of the adjoint equation and the relationship between two Hamiltonian functions. As applications, we use the theoretical results to an indefinite linear quadratic (LQ) Pareto game with general delays. [ABSTRACT FROM AUTHOR]

Fisheries, as indispensable natural resources for human, need to be managed with both short‐term economical benefits and long‐term sustainability in consideration. This has remained a challenge, because the population and catch dynamics of the fisheries are complex and noisy, while the data available is often scarce and only provides partial information on the dynamics. To address these challenges, we formulate the population and catch dynamics as a Partially Observable Markov Decision Process (POMDP), and propose a model‐based offline reinforcement learning approach to learn an optimal management policy. Our approach allows learning fishery management policies from possibly incomplete fishery data generated by a stochastic fishery system. This involves first learning a POMDP fishery model using a novel least squares approach, and then computing the optimal policy for the learned POMDP. The learned fishery dynamics model is useful for explaining the resulting policy's performance. We perform systematic and comprehensive simulation study to quantify the effects of stochasticity in fishery dynamics, proliferation rates, missing values in fishery data, dynamics model misspecification, and variability of effort (e.g., the number of boat days). When the effort is sufficiently variable and the noise is moderate, our method can produce a competitive policy that achieves 85% of the optimal value, even for the hardest case of noisy incomplete data and a misspecified model. Interestingly, the learned policies seem to be robust in the presence of model learning errors. However, non‐identifiability kicks in if there is insufficient variability in the effort level and the fishery system is stochastic. This often results in poor policies, highlighting the need for sufficiently informative data. We also provide a theoretical analysis on model misspecification and discuss the tendency of a Schaefer model to overfit compared with a Beverton–Holt model. [ABSTRACT FROM AUTHOR]

Energy efficiency in computation is ultimately limited by noise, with quantum limits setting the fundamental noise floor. Analog physical neural networks hold promise for improved energy efficiency compared to digital electronic neural networks. However, they are typically operated in a relatively high-power regime so that the signal-to-noise ratio (SNR) is large (>10), and the noise can be treated as a perturbation. We study optical neural networks where all layers except the last are operated in the limit that each neuron can be activated by just a single photon, and as a result the noise on neuron activations is no longer merely perturbative. We show that by using a physics-based probabilistic model of the neuron activations in training, it is possible to perform accurate machine-learning inference in spite of the extremely high shot noise (SNR ~ 1). We experimentally demonstrated MNIST handwritten-digit classification with a test accuracy of 98% using an optical neural network with a hidden layer operating in the single-photon regime; the optical energy used to perform the classification corresponds to just 0.038 photons per multiply-accumulate (MAC) operation. Our physics-aware stochastic training approach might also prove useful with non-optical ultra-low-power hardware. Neural networks on analog physical devices often struggle with low computational precision. Here, authors developed an approach that enables neural networks to effectively exploit highly stochastic systems, achieving high performance even under an extremely low signal-to-noise ratio. [ABSTRACT FROM AUTHOR]

Swarm intelligence has become a popular framework for developing new metaheuristics or stochastic optimization methods in recent years. Many swarm-based metaheuristics are developed by employing multiple searches whether it is conducted through swarm split, serial searches, stochastic choose. Unfortunately, many existing studies that introduced new metaheuristic focused on assessing the performance of the proposed method as a single package. On the other hand, the contribution of each search constructing the metaheuristic is still unknown as the consequence of the missing of single or individual search assessment. Based on this problem, this work is aimed to investigate the performance of five directed searches that are commonly found in recent swarm-based metaheuristics individually. These five searches include: motion toward the highest quality member, motion relative to a randomly chosen member, motion relative to a random solution along the space, motion toward a randomly chosen higher quality member, and motion toward the middle among higher quality members. In this assessment, these five searches are challenged to find the optimal solution of 23 classic functions. The result shows that the first, fourth, and five searches perform better than the second and third searches. [ABSTRACT FROM AUTHOR]

This study focuses on time-delayed zero-sum games (ZSGs). Firstly, a zero-sum game (ZSG) for a time-delayed uncertain stochastic system is investigated. An approach is proposed to translate the time-delayed uncertain stochastic ZSG into an equivalent uncertain stochastic game without time delay. Then recursive equations are proposed accordingly to transform the uncertain stochastic game into a solution problem for deterministic difference equations. Based on recursive equations and chance theory, exact solutions for the saddle-point equilibrium solutions of ZSGs for time-delayed uncertain stochastic systems considering linear, quadratic and cubic control terms are provided. Finally, we illustrate the effectiveness of our approach to the time-delayed uncertain stochastic ZSGs through numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, a more effective and faster iterative algorithm is put forward to find the solution of stochastic coupled Riccati matrix equations concerning It$ \hat{o} $ stochastic systems with Markovian jump. This algorithm is inspired by the idea of the successive over-relaxation (SOR) method, and the property of convergence is mainly based on the principle of mathematical induction. Then, an initialization method is discussed to start the algorithm. Furthermore, two numerical examples are presented to show the superiority of this algorithm on the speed of convergence compared to other previous algorithms. [ABSTRACT FROM AUTHOR]

This study investigates the impact of outliers on the evolution of clusters in temporal data-sets. Monitoring and tracing cluster transitions of temporal data sets allow us to observe how clusters evolve and change over time. By tracking the movement of data points between clusters, we can gain insights into the underlying patterns, trends, and dynamics of the data. This understanding is essential for making informed decisions and drawing meaningful conclusions from the clustering results. Cluster evolution refers to the changes that occur in the clustering results over time due to the arrival of new data points. The changes in cluster solutions are classified as external and internal transitions. The study employs the survival ratio and history cost function to investigate the effects of outliers on changes experienced by the clusters at successive time points. The results demonstrate that outliers have a significant impact on cluster evolution, and appropriate outlier handling techniques are necessary to obtain reliable clustering results. The findings of this study provide useful insights for practitioners and researchers in the field of stream clustering and can help guide the development of more robust and accurate stream clustering algorithms. [ABSTRACT FROM AUTHOR]

ABSTRACT This study proposes a filtering based maximum likelihood generalized extended gradient algorithm for multivariable nonlinear systems with autoregressive moving average noises. The parameter estimates are obtained by minimizing the half squared residual measurement which can approach the true values. An auxiliary model is also established with the measurable information of the system, and the output of the auxiliary model is used to replace the unmeasurable variables of the system, so that the output of the auxiliary model approximates these unmeasurable variables, so as to obtain the consistent estimation of the system parameters. A maximum likelihood generalized extended gradient algorithm is derived for comparison and a numerical example is provided to show the effectiveness of the proposed method and the estimates converge to the actual values quickly. [ABSTRACT FROM AUTHOR]

This manuscript explores the stability theory of several stochastic/random models. It delves into analyzing the stability of equilibrium states in systems influenced by standard Brownian motion and exhibit random variable coefficients. By constructing appropriate Lyapunov functions, various types of stability are identified, each associated with distinct stability conditions. The manuscript establishes the necessary criteria for asymptotic mean-square stability, stability in probability, and stochastic global exponential stability for the equilibrium points within these models. Building upon this comprehensive stability investigation, the manuscript delves into two distinct fields. Firstly, it examines the dynamics of HIV/AIDS disease persistence, particularly emphasizing the stochastic global exponential stability of the endemic equilibrium point denoted as , where the underlying basic reproductive number is greater than one (). Secondly, the paper shifts its focus to finance, deriving sufficient conditions for both the stochastic market model and the random Ornstein–Uhlenbeck model. To enhance the validity of the theoretical findings, a series of numerical examples showcasing stability regions, alongside computer simulations that provide practical insights into the discussed concepts are provided. [ABSTRACT FROM AUTHOR]

This article discusses a finite-source stock-dependent stochastic inventory system with multiple servers and a retrial facility. The system can store a maximum of S items, and the lifetime of each item is exponentially distributed. The primary customer arrives at the waiting hall from the finite source and receives service from multi-servers. The rate at which customers arrive depends on the current stock level. If the waiting hall is full during the primary customer's arrival, he enters the finite orbit. Additionally, customers in the waiting hall may lose patience and enter the orbit. To replenish the stock, we follow the (s, Q) ordering policy. We calculate the joint probability distribution of the number of inventory items, busy servers, and number of customers in the waiting hall and orbit at a steady state. We conduct a comparative numerical analysis to determine the impact of heterogeneous and homogeneous service rates on various metrics, such as the average impatient customer rate, the fraction of successful retrials, and the average number of customers in the waiting hall and orbit. [ABSTRACT FROM AUTHOR]

The well-posedness and exponential ergodicity are proved for stochastic Hamiltonian systems containing a singular drift term which is locally integrable in the component with noise. As an application, the well-posedness and uniform exponential ergodicity are derived for a class of singular degenerated McKean-Vlasov SDEs. [ABSTRACT FROM AUTHOR]

ABSTRACT This article considers a distributed identification problem for linear stochastic systems whose input and output observations are scheduled by an adaptive event‐triggered scheme. An event detector with time‐varying thresholds is designed to control the transmission of measurements from the sensors to the estimators, which leads to that only a subset of input and output data is available for identification. The estimators exchange information over a network and cooperatively identify the unknown parameters. A distributed recursive identification algorithm under the event‐triggered scheme is proposed based on the distributed stochastic approximation algorithm with expanding truncations (DSAAWET). Under mild assumptions, the strong consistency of the algorithm is proved, that is, the estimates generated from each estimator achieve consensus and converge to the true parameters with probability one. Finally, two numerical examples are provided to validate the theoretical results of the algorithm. [ABSTRACT FROM AUTHOR]

This study is concerned with the influence of astronomical forcing and stochastic disturbances on non-linear dynamics of the Earth's climate. As a starting point, we take the system of climate equations derived by Saltzman and Maasch for late Cenozoic climate changes. This system contains variations of three prognostic variables: the global ice mass, carbon dioxide concentration, and deep ocean temperature. The bifurcation diagram of deterministic system shows possible existence/coexistence of stable equilibria and limit cycle leading either to monostability or bistability. Fitting the astronomical forcing by an oscillatory function and representing the deep ocean temperature deviations by means of white Gaussian noise of various intensities, we analyze the corresponding stochastic system of Saltzman and Maasch equations for the deviations of prognostic variables from their average values (equilibrium state). The main conclusions of our study are as follows: (i) astronomical forcing causes the climate system transitions from large-amplitude oscillations to small-amplitude ones and vice versa; (ii) astronomical and stochastic forcings together cause the mixed-mode climate oscillations with intermittent large and small amplitudes. In this case, the Earth's climate would be shifting from one stable equilibrium with a warmer climate to another stable equilibrium with a colder climate and back again. [ABSTRACT FROM AUTHOR]

Stochastic collocation (SC) is a well‐known non‐intrusive method of constructing surrogate models for uncertainty quantification. In dynamical systems, SC is especially suited for full‐field uncertainty propagation that characterizes the distributions of the high‐dimensional solution fields of a model with stochastic input parameters. However, due to the highly nonlinear nature of the parameter‐to‐solution map in even the simplest dynamical systems, the constructed SC surrogates are often inaccurate. This work presents an alternative approach, where we apply the SC approximation over the dynamics of the model, rather than the solution. By combining the data‐driven sparse identification of nonlinear dynamics framework with SC, we construct dynamics surrogates and integrate them through time to construct the surrogate solutions. We demonstrate that the SC‐over‐dynamics framework leads to smaller errors, both in terms of the approximated system trajectories as well as the model state distributions, when compared against full‐field SC applied to the solutions directly. We present numerical evidence of this improvement using three test problems: a chaotic ordinary differential equation, and two partial differential equations from solid mechanics. [ABSTRACT FROM AUTHOR]

Although traditional active suspension can offer superior riding comfort and maneuverability over its semiactive and passive counterparts, its reliance on an external power supply has hindered its widespread applications in vehicles. To overcome this deficiency, this paper proposes an innovative self-powered active suspension design for a high-speed train (HST), by leveraging the recently emerging H-bridge circuit-based electromagnetic damper (HB-EMD), allowing bidirectional power flow between the damper and controlled system. The capability of HB-EBD to achieve unique self-powered active skyhook control was previously proved in a simplified single degree-of-freedom (SDOF) structure under harmonic excitations; however, the feasibility of employing HB-EMD to realize active vibration control for more complex structural systems under stochastic excitations remains an unanswered question. One main challenge is designing a novel control algorithm that can simultaneously realize vibration control and self-powering objectives, which is unattainable by traditional active control algorithms. In this study, an ad hoc model predictive controller (MPC) is designed to guarantee the fulfillment of these dual objectives. To evaluate the performance of the proposed active suspension design, two separate HB-EMDs are implemented on the front and rear sides of the secondary lateral suspensions of an HST model subjected to stochastic track irregularities. At a speed of 200km/h, the proposed HB-EMDs with MPC could achieve a 55% reduction in the lateral acceleration of the car body in comparison with passive suspension, meanwhile maintaining energy harvesting performance with an average output power of 25.0W. In contrast, a traditional active linear quadratic Gaussian (LQG) controller consumes 72.7W power when performing comparable vibration reduction. This study, for the first time, validates the feasibility of designing a self-powered, actively controlled secondary lateral HST suspension system without relying on an external power source, which will potentially pave the way for a new active vibration control paradigm for other generic structures. [ABSTRACT FROM AUTHOR]

The dynamics of plant-insect interactions play a crucial role in the ecosystem, influenced by complex molecular signaling pathways. This study extends existing deterministic models of plant-insect systems by incorporating stochastic elements and molecular interactions, particularly focusing on the roles of Botrytis Induced Kinase-1 (BIK1) and Phyto Alexin Deficient-4 (PAD4) proteins. The model evaluates the effects of constant inhibition, pulsed inhibition, and adaptive feedback control on plant biomass ( y 1 ) , insect herbivore density ( y 2 ) , PAD4 levels ( y 3 ) , and BIK1 levels ( y 4 ). Additionally, we examine the impact of different noise types, including deterministic, Gaussian, and Lévy noise, on system variability and stability. Results indicate that our stochastic model is superior as it shows a significant reduction in BIK1 levels, particularly under higher noise intensities, which enhances PAD4 activity and improves plant defense mechanisms. Moreover, moderate noise intensity (σ = 0.05) provides an optimal balance, sustaining PAD4 levels while effectively controlling insect herbivore populations. We also integrate MEMS-based feedback mechanisms, which dynamically adjust plant biomass and molecular signaling, further stabilizing the system's response to environmental variability. [ABSTRACT FROM AUTHOR]

ABSTRACT In this paper, we investigate observer‐based switching‐like adaptive‐triggered resilient state feedback control for discrete singular systems under deception‐injection (DI) attacks. Considering state variables are not completely measurable, a delayed state observer is engineered to reconstruct system states and the occurrence of DI attacks is described by Bernoulli random variables. The upper bound method is used to deal with the DI attacks with jumping patterns and imprecise occurrence probabilities. Taking into account the sporadic nature of DI attacks, switching‐like adaptive‐triggered resilient control method is presented, and the collaboratively designed triggered mechanism and resilient control strategy can not only automatically adjust data transmission based on the system states, but also save communication resources and network bandwidth, and enhance the tolerance to hostile attacks so as to improve safety and reliability of networked singular systems. By utilizing singular value decomposition technique, the noncausal behavior of the singular system is avoided and by applying linear matrix inequality (LMI) technology, the desired gains of controller and observer are achieved concurrently, then neoteric conditions about H∞$$ {H}_{\infty } $$ stochastic admissibility of closed‐loop discrete singular systems are provided. Ultimately, the validity of the proposed resilient coordination control approach is verified via a direct current (DC) motor model. [ABSTRACT FROM AUTHOR]

ABSTRACT This article seeks the enhancement of nonlinearity tolerance in time/event‐triggered stabilization for stochastic systems. In the related results, the controller functions are required to obey global Lipschitz condition for the suppression of sampling/execution error, and the drift and/or diffusion coefficients of the stochastic systems are restricted to polynomial or, even, linear growth. These limitations deserve overcoming for enlarged applications. To this end, a distinct framework of time/event‐triggered controls is established for stochastic systems, targeted at exponential stabilization. Specifically, inclusive Lyapunov‐type feasibility conditions are proposed by capturing the effect of sampling/execution error and distinguishing the role of system nonlinearities. Particularly, different from the related results, the evolution of sampling/execution error is subtly exploited via Lyapunov functions to reveal the dynamic interaction between the sampling/execution errors and system state. Then, time‐triggered exponential stabilization via sampled‐data controller is achieved not only in the moment sense but also in the almost sure sense. Accordingly, Lyapunov function based analysis is performed for the composite dynamics of system state and sampling error, confronted with the coupling of discontinuous and stochastic features. To further reduce execution, periodic event‐triggered control is exploited to achieve exponential stabilization for stochastic nonlinear systems, by virtue of the relation with the dynamic evolution under sampled‐data control. Through typical examples, we demonstrate the potential of our framework in handling the cases with the controller functions violating global Lipschitz condition and with the system nonlinearities beyond polynomial growth. [ABSTRACT FROM AUTHOR]

In this study, we conduct a comprehensive investigation of the novel characteristics of the (2 + 1)-dimensional stochastic Hirota–Maccari System (SHMS), which is a prominent mathematical model with significant applications in the field of nonlinear science and applied mathematics. Specifically, SHMS plays a critical role in the study of soliton dynamics, nonlinear wave propagation, and stochastic effects in complex physical systems such as fluid dynamics, optics, and plasma physics. In order to account for the abrupt and significant fluctuation, the aforementioned system is investigated using a Wiener process with multiplicative noise in the Itô sense. The considered equation is studied by the new extended direct algebraic method (NEDAM) and the modified Sardar sub-equation (MSSE) method. By solving this equation, we systematically derived the novel soliton solutions in the form of dark, dark-bright, bright-dark, singular, periodic, exponential, and rational forms. Additionally, we also categorize and analyze the W-shape, M-shape, bell shape, exponential, and hyperbolic soliton wave solutions, which are not documented by researchers. The bifurcation, chaos and sensitivity analysis has been depicted which represent the applicability of the system in different dynamics. These findings greatly advance our knowledge of nonlinear wave events in higher-dimensional stochastic systems both theoretically and in terms of possible applications. These findings are poised to open new avenues for future research into the applicability of stochastic nonlinear models in various scientific and industrial domains. [ABSTRACT FROM AUTHOR]

ABSTRACT In this work, the stability problem of nonlinear stochastic systems is investigated under exogenous disturbances through event‐triggered impulsive control (ETIC). The ETIC strategy proposed in this paper incorporates three levels of events, taking into account four indicators: threshold, control‐free index, inspection interval, and waiting time for stochastic systems, which is more practically significant and can effectively eliminate the Zeno behavior. By utilizing Lyapunov stability theory, stochastic analysis techniques, and some fundamental inequalities, sufficient conditions for the rth$$ r\mathrm{th} $$ moment input‐to‐state stability (r$$ r $$‐ISS) and exponentially r$$ r $$‐ISS of the considered system can be achieved through the implementation of the designed ETIC. Then, the theoretical results are employed in actual nonlinear stochastic systems, leading to the establishment of LMI‐based criteria for exponential r$$ r $$‐ISS. Ultimately, the feasibility of ETIC strategy is confirmed through two instances. [ABSTRACT FROM AUTHOR]

During flight, projectiles are subject to uncertainties such as aerodynamic forces, wind gusts, and measurement errors; all of which significantly affect their stability and accuracy. As a result, studying the response of projectile systems under stochastic excitation is essential. This paper focuses on the solution and analysis of projectile system responses under stochastic excitation. We employed the path integral method to compute the transient and stationary probability density functions for projectile systems subjected to Gaussian stochastic external and parametric excitations. Based on the probabilistic responses, we analyzed the evolution of the system's probability density function over time under Gaussian white noise excitation, as well as the changes in the stationary probability density function with air density and flight speed as bifurcation parameters. The analysis results indicate that within a specific range of parameter variations, air density can induce stochastic P‐bifurcation phenomena. Furthermore, increasing air density and flight speed can enhance the stability of the projectile. [ABSTRACT FROM AUTHOR]