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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]

This paper studies the problem of state feedback stabilisation, in the sense of a weak solution, for a class of multi-input affine control stochastic systems whose drift and diffusion terms are dependent on the control and for which classical methods are not applicable. Based on the generalised stochastic Lyapunov theorem and on the technique of stochastic control Lyapunov functions, sufficient conditions for the existence of a continuous stabilising feedback control are proposed, and a state feedback controller can be developed to guarantee the closed-loop system globally asymptotically stable in probability. This work generalises previous results on the stabilisation of single-input affine control stochastic systems. The obtained results are illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

The human immune system can recognize, attack, and eliminate cancer cells, but cancers can escape this immune surveillance. Variants of ecological predator–prey models can capture the dynamics of such cancer control mechanisms by adaptive immune system cells. These dynamical systems describe, e.g., tumor cell-effector T cell conjugation, immune cell activation, cancer cell killing, and T cell exhaustion. Target (tumor) cell-T cell conjugation is integral to the adaptive immune system's cancer control and immunotherapy. However, whether conjugate dynamics should be explicitly included in mathematical models of cancer-immune interactions is incompletely understood. Here, we analyze the dynamics of a cancer-effector T cell system and focus on the impact of explicitly modeling the conjugate compartment to investigate the role of cellular conjugate dynamics. We formulate a deterministic modeling framework to compare possible equilibria and their stability, such as tumor extinction, tumor-immune coexistence (tumor control), or tumor escape. We also formulate the stochastic analog of this system to analyze the impact of demographic fluctuations that arise when cell populations are small. We find that explicit consideration of a conjugate compartment can (i) change long-term steady-state, (ii) critically change the time to reach an equilibrium, (iii) alter the probability of tumor escape, and (iv) lead to very different extinction time distributions. Thus, we demonstrate the importance of the conjugate compartment in defining tumor-effector T cell interactions. Accounting for transitionary compartments of cellular interactions may better capture the dynamics of tumor control and progression. [ABSTRACT FROM AUTHOR]

We propose a systematic approach to construct a new family of stochastic symplectic schemes for the strong approximation of the solution of stochastic Hamiltonian systems. Our approach is based both on B-series and generating functions. The proposed schemes are a generalization of the implicit midpoint rule, they require derivatives of the Hamiltonian functions of at most order two, and are constructed by defining a generating function. We construct some schemes with strong convergence order one and a half, and we illustrate numerically their long term performance. [ABSTRACT FROM AUTHOR]

The trade off analysis between the fixed‐time stabilization in probability and energy consumption of nonlinear stochastic system is studied in this paper. By constructing a switching controller and using inequality techniques, sufficient conditions for fixed‐time stabilization in probability in the Lyapunov sense are given, and the upper bounds of the settling time function and energy consumption are estimated. Then, by analyzing the relationship between control parameters, control time and energy consumption, the existence of trade off between control time and energy consumption is proposed, and the corresponding optimal parameter values are given. Finally, a numerical example is used to verify the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the event‐triggered generalized extended state observer‐based estimation issue for a class of nonlinear networked control systems with unmodeled dynamics, external disturbances and multi‐channel attacks. In order to resist different forms of attack threats on multiple communication channels from sensors to the observer, Markov chain is introduced to describe the stochastic switching or jumping behavior between different attack modes. Considering the limited network resources, the measured outputs are transmitted to the observer only when the triggering conditions are met. Moreover, the parameters modeled by the Bernoulli process are adopted to help analyze potential random gain variations of the generalized extended state observer. By employing Lyapunov stability theory and stochastic systems analysis, sufficient conditions are derived to ensure that the augmented system is exponentially bounded in mean square, and the expected observer gains are further determined through linear matrix inequalities. Finally, a numerical example and a simulation related to the RLC series circuit system are conducted, illustrating the proposed method's effectiveness. [ABSTRACT FROM AUTHOR]

This paper offers a concise overview of the existing literature on efficiency and productivity, focusing on stochastic frontier models. The emphasis is placed on technical inefficiency (TI), defined as the failure to produce the maximum output given inputs, and allocative inefficiency (AI), arising from non-optimal input utilization. The primary objective of this brief survey is to assist readers in grasping the fundamental concepts of modelling TI and AI within single and/or multiple output production technologies. Additionally, attention is given to the challenges associated with computing the cost of AI (CAI) in primal-based models, as well as modelling CAI within dual cost and profit functions. [ABSTRACT FROM AUTHOR]

This paper presents one of the most interesting generalizations of Gaver's basic two-unit parallel system sustained by a cold standby unit and attended by a repairman with multiple vacations. The system was studied using the supplementary variables technique, like many other similar semi-Markov systems. D.P. Gaver, Jr. was the first to apply this method for constructing and studying reliability models, and since then it has been then widely used by other researchers to study various reliability problems. As a result, non-classical boundary value problem of mathematical physics with nonlocal boundary conditions has been obtained. Until now, a solution to this problem was obtained in terms of Laplace transforms. Naturally, the most significant part of the problem is a system of partial differential equations (Kolmogorov forward equations). In this study, we demonstrate that Kolmogorov equations are redundant and we can solve the problem by avoiding the necessity of using them. We present here a novel, purely probabilistic approach. The results are formulated as rigorous mathematical statements, offering a significant simplification in the reliability analysis of stochastic systems. Our findings show that this novel approach can be applied to study both semi-Markov and some non semi-Markov models where the supplementary variables technique is used. [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 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]

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 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]

The existence-uniqueness theory for solutions to stochastic dynamic systems is always a significant theme and has received tremendous attention. This article aims to study the theory for stochastic functional differential equations (SFDEs) driven by the G-Lévy process. It derives the existence-uniqueness theorem for solutions to SFDEs driven by the G-Lévy process. Moreover, it shows the error estimation between the exact solution x (t) and Picard approximate solutions x n (t) , n ≥ 1 . Ultimately, the exponential estimate has been derived. [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]

The document discusses the significance of stochastic processes in various scientific disciplines and their mathematical interpretation of randomness and probabilistic analysis. It highlights the historical development of stochastic processes, starting with Brownian motion and the contributions of key figures like Louis Bachelier, Andrei Kolmogorov, Joseph Doob, and William Feller. The text also honors the distinguished mathematician Prof. Sally McClean for her significant contributions to mathematical modeling and health care planning, showcasing her research achievements and recognition in the field. Additionally, the document provides an overview of articles in a special volume dedicated to stochastic processes, categorized into key thematic areas like Markov Chains, Semi-Markov Chains, Mathematical Optimization, and General Stochastic Processes, with brief descriptions of selected articles in each category. [Extracted from the article]

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]

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]

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]

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]

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]

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]

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]

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]

In this paper, we develop a stochastic multi-molecule chemical reaction model with reaction rate perturbed by log-normal O r n s t e i n - U h l e n b e c k process in order to consider the effects of random factors on chemical reaction dynamics. Firstly, we prove the existence and uniqueness of the global positive solution for the stochastic model. In addition, we obtain the conditions under which the corresponding stochastic system exist a stationary distribution. Then, we derive a sufficient condition to end the reaction. Furthermore, the stochastic system has been transformed into a linearized system, by solving F o k k e r - P l a n c k equation, we obtain the exact expression of the density function around the quasi-equilibrium of this system. Finally, we draw a conclusion that the dynamical behaviors of the stochastic system will be affected by random factor, O r n s t e i n - U h l e n b e c k process respectively [ABSTRACT FROM AUTHOR]

The existing research studies on the basin stability of stochastic systems typically focus on smooth systems, or the attraction basins are pre-defined as easily solvable regular basins. In this work, we introduce a new framework to discover the basin stability from state time series in the non-smooth stochastic competition system under threshold control. Specifically, we approximate the drift and diffusion with threshold control parameters by an extended Kramers–Moyal expansion with initial state partitioning. Then, we calculate the first transition probability of irregular attraction basins by applying a difference scheme and smooth approximation methods for the system. Numerical simulations of the original system validate the accuracy of the identified drift and diffusion terms, as well as the smooth approximation. Our findings reveal that threshold control modifies the influence of environmental noise on the system basin stability. [ABSTRACT FROM AUTHOR]

In gas-to-methanol processes, optimizing multi-energy systems is a critical challenge toward efficient energy allocation. This paper proposes an entropy-based stochastic optimization method for a multi-energy system in a gas-to-methanol process, aiming to achieve optimal allocation of gas, steam, and electricity to ensure executability under modeling uncertainties. First, mechanistic models are developed for major chemical equipments, including the desulfurization, steam boilers, air separation, and syngas compressors. Structural errors in these models under varying operating conditions result in noticeable model uncertainties. Second, Bayesian estimation theory and the Markov Chain Monte Carlo approach are employed to analyze the differences between historical data and model predictions under varying operating conditions, thereby quantifying modeling uncertainties. Finally, subject to constraints in the model uncertainties, equipment capacities, and energy balance, a multi-objective stochastic optimization model is formulated to minimize gas loss, steam loss, and operating costs. The entropy weight approach is then applied to filter the Pareto front solution set, selecting a final optimal solution with minimal subjectivity and preferences. Case studies using Aspen Hysys-based simulations show that optimization solutions considering model uncertainties outperform the counterparts from a standard deterministic optimization in terms of executability. [ABSTRACT FROM AUTHOR]

In this work, we are devoted to discussing a system of fractional stochastic differential variational inequalities with Lévy jumps (SFSDVI with Lévy jumps), that comprises both parts, that is, a system of stochastic variational inequalities (SSVI) and a system of fractional stochastic differential equations(SFSDE) with Lévy jumps. Here it is noteworthy that the SFSDVI with Lévy jumps consists of both sections that possess a mutual symmetry structure. Invoking Picard's successive iteration process and projection technique, we obtain the existence of only a solution to the SFSDVI with Lévy jumps via some appropriate restrictions. In addition, the major outcomes are invoked to deduce that there is only a solution to the spatial-price equilibria system in stochastic circumstances. The main contributions of the article are listed as follows: (a) putting forward the SFSDVI with Lévy jumps that could be applied for handling different real matters arising from varied domains; (b) deriving the unique existence of solutions to the SFSDVI with Lévy jumps under a few mild assumptions; (c) providing an applicable instance for spatial-price equilibria system in stochastic circumstances affected with Lévy jumps and memory. [ABSTRACT FROM AUTHOR]

To ascertain energy availability and system performance, a comprehensive understanding of the systems' degradation profile and impact on overall plant reliability is imperative. The current study presents an integrated Failure Mode and Effects Analysis (FMEA)–Markovian algorithm for reliability-based instantaneous energy performance prediction for thermal energy systems. The FMEA methodology is utilized to identify and categorize the various failure modes of the gas turbines, establishing a reliability pattern that informs overall system performance. Meanwhile, the Markovian algorithm discretizes the system into states based on its operational energy performance envelope. The algorithm predicts instantaneous energy performance according to upper and lower bounds criteria. This integrated methodology has been subjected to testing in three case studies, yielding results that demonstrate improved reliability and instantaneous energy performance prediction during system degradation. It was observed that after 14 years of operation, the likelihood of major failures increases to 79.6%, 88.7%, and 82.8%, with corresponding decreases in system performance reliability of 10.1%, 4.5%, and 7.8% for the Afam, Ibom, and Sapele gas turbine plants, respectively. Furthermore, the percentage of instantaneous mean power performance relative to the rated capacity is 37.9%, 35.1%, and 46.3% for the three gas turbine plants. These results indicate that the Sapele thermal power plant performs better relative to its rated capacity. Overall, this integrated methodology serves as a valuable tool for monitoring gas turbine engine health and predicting energy performance under varying operating conditions. [ABSTRACT FROM AUTHOR]

Metasurface-based imaging is attractive due to its low hardware costs and system complexity. However, most of the current metasurface-based imaging systems require stochastic wavefront modulation, complex computational post-processing, and are restricted to 2D imaging. To overcome these limitations, we propose a scanning virtual aperture imaging system. The system first uses a focused beam to achieve near-field focal plane scanning, meanwhile forming a virtual aperture. Secondly, an adapted range migration algorithm (RMA) with a pre-processing step is applied to the virtual aperture to achieve a 3D high-resolution reconstruction. The pre-processing step fully exploits the feature of near-field beamforming that only a time delay is added on the received signal, which introduces ignorable additional calculation time. We build a compact prototype system working at a frequency from 38 to 40 GHz. Both the simulations and the experiments demonstrate that the proposed system can achieve high-quality imaging without complex implementations. Our method can be widely used for single-transceiver coherent systems to significantly improve the imaging depth of field (DOF). [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]

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]

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]

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]

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]

This paper considers the exact controllability of Itô stochastic systems with input delay. In particular, one delay-free controller and one delayed controller are involved in the systems which complicates the study due to the inconsistency of adaptiveness caused by input delay. The main contribution of this paper is to provide the necessary and sufficient Gramian matrix condition and the necessary Rank condition for the exact controllability. The key is to solve the backward stochastic differential equations (BSDEs) with input delay. • The novelty is to study the controllability of stochastic systems with input delay. • The main contribution is to present the exact controllability criterion. • The key is the solvability of backward stochastic equation with input delay. [ABSTRACT FROM AUTHOR]

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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]