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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]

This paper is concerned with the pathwise dynamics of stochastic p -Laplacian lattice systems driven by Wong-Zakai type approximation noises. The existence and uniqueness of pullback random attractor are established for the approximate system with a wide class of nonlinear diffusion term. When the stochastic system is driven by a linear multiplicative noise, we prove the convergence of solutions and the upper semicontinuity of random attractors for Wong-Zakai approximations as the step-length of the Wiener shift approaches zero. [ABSTRACT FROM AUTHOR]

An ecosystem with anti-predator behavior is established in both deterministic and stochastic environments. This means that adult prey could attack weak predators. Bifurcation diagrams are used to analyze the deterministic case, while a tool called the most probable trajectory, defined by the spatial extreme point of the probability density function (PDF), is employed to explore the stochastic case. The Fokker-Planck equation is solved using the stochastic averaging method of energy envelope, which provides an analytical expression for the PDF. The results show that in the deterministic case, effective anti-predator behavior can dampen predator-prey oscillations and mitigate negative effects caused by the time delay. Additionally, it can accelerate the transient solution to reach a steady state and reduce the ratio of predator-to-prey densities in coexistence. In the stochastic case, effective anti-predator behavior can raise the noise threshold that leads to population extinction. Furthermore, it can also reduce the randomness of solutions. It's worth noting that appropriate anti-predator behavior can ensure that the most probable solution in the stochastic system approximates the solution in the deterministic system. Monte Carlo simulations verify the accuracy of these analytical results. [ABSTRACT FROM AUTHOR]

In this paper, the μ-state estimation issue for Markovian switching complex-valued neural networks with mixed delays has been addressed. To conserve communication resources, an effective event-triggered mechanism is proposed, which relays on a Markovian switching positive threshold. By resorting to Lyapunov stability theory, stochastic analysis method and matrix inequalities technique, some sufficient criteria are established to guarantee the estimation error system is stochastic μ-stable in the mean sense. Moreover, the expected estimator gain matrices can be accurately achieved by solving some obtained matrix inequalities. Besides, it is should be pointed that the μ-stability involves exponential, power, and logarithmic stability, which expands a mass of existed relevant results. In the end, for power stability, one numerical example is provided to substantiate the effectiveness and credibility of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this technical note, the problem of the extended dissipative control for interval type-2 fuzzy model with nonlinear network systems in the event-triggered framework is investigated. A novel dynamic event-triggered strategy is developed to ascertain the instants of activation. It has the advantage of reducing data transmission and optimising the utilisation of communication resources. On the basis of the proposed mechanism, the stochastic Lyapunov function including internal dynamic variables is constructed. Based on this function, coupled with the inequality scaling technique and the application of Dynkin's formula, we derive a sufficient condition for the system's stochastic asymptotic stability and extended dissipativity. The design of the dynamic event-triggered extended dissipative controller becomes challenging because the new sufficient condition is nonlinear for some matrix variables. However, utilising the Projection Lemma and the co-design approach, such a controller can be developed based on the obtained analysis result. The methodology is demonstrated through a rigorous numerical simulation case study. [ABSTRACT FROM AUTHOR]

This paper investigates the asymptotic stability of neutral stochastic pantograph systems with Markovian switching (NSPSMS). The stochastic LaSalle theorem has been set up to locate the attractive sets for NSPSMS without linear growth condition. Subsequently, combining the stochastic LaSalle theorem and uniformly continuous theory, almost surely asymptotic stability and pth moment asymptotic stability are analysed. Furthermore, we also present one new criterion on the pth moment polynomial stability and almost surely polynomial stability for NSPSMS, where the coefficients of the delay term are time invariable. Finally, three examples are provided to exhibit the efficiency of the proposed results. [ABSTRACT FROM AUTHOR]

The classical PID (proportional‐integral‐derivative) control is the most basic and widely used control algorithm in engineering systems by far. Whether PID control can effectively deal with coupled multiagent uncertain nonlinear dynamics is well worth investigating. In this article, a class of PID controlled multiagent stochastic systems with coupled uncertain dynamics is considered, where the control input is nonaffine. Each agent has its own regulation objective, and only has access to its own regulation error information for PID feedback. First, a PID parameter set will be constructed explicitly based on some prior knowledge about the nonlinear functions, such that the overall multiagent system can be stabilized globally in the mean square sense, as long as the PID parameters are chosen from the constructed set. Moreover, the regulation error will be proven to have an upper bound proportional to the noise intensity along the reference signal. Furthermore, it will be shown that the regulation error of each agent can be arbitrarily small by choosing the PID parameters suitably large. Finally, the theoretical results will be verified by simulations. [ABSTRACT FROM AUTHOR]

This article considers the parameter identification problems of stochastic systems which described by the finite impulse response moving average model. Since the system is disturbed by colored noise, we introduce the data filtering technique from a view point of improving the parameter estimation accuracy. The data filtering technique is to use a filter to filter the input and output data of the system disturbed by colored noise so as to improve the identification accuracy. By using the data filtering technique, this article proposes a filtering‐based recursive extended least squares (F‐RELS) algorithm. The convergence analysis indicates that the parameter estimates can converge to their true values. Compared with the recursive extended least squares algorithm, the proposed F‐RELS algorithm can obtain more accurate parameter estimation. Finally, a numerical simulation example is given to demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this article, a class of global finite‐time stabilization problem for high‐order stochastic nonlinear systems with multiple unknown control directions is studied. In order to solve the difficulties caused by the unknown control directions and at the same time, the system is required to converge to the origin in a limited time. Therefore, a new switching mechanism based on the Lyapunov‐like function is proposed. By adding a power integral technique and utilizing sign function, a finite‐time switching controller is designed. The controller parameters need to be adjusted online according to the proposed switching logic. It is rigorously proved that the designed controller can make the system state converge probabilistically to the origin in a finite‐time. A simulation example shows the effectiveness of the proposed control algorithm. [ABSTRACT FROM AUTHOR]

This paper designs an adaptive event‐triggered output‐feedback controller for a class of p$$ p $$‐normal switched SNS with uncertain output function and time‐varying delays. Firstly, a Lyapunov function and reduced‐order observer using the output signal are constructed for nominal system by virtue of sign function and API technique. Then a dynamic gain and time‐decaying parameter are introduced into the event‐triggered mechanism to reduce the number of control updates. Next, by virtue of LKF and stochastic Barbalat's Lemma, it is proved that all the signals are bounded and system states asymptotically converge to zero in probability, and Zeno behavior is excluded. Finally, a numerical example and practical one are given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper is devoted to the stochastic travelling wave solutions of a three-species competitive–cooperative system with multiplicative noise. The existence of the travelling wave solutions can be proved by constructing upper/lower-solution and stochastic dynamical systems theory. Moreover, under the more restricted assumption on the coefficients of system, and applying Feynman–Kac formula and upper/lower solution technique, the upper/lower bounds of the asymptotic wave speed can be provided. [ABSTRACT FROM AUTHOR]

As the adoption of digital twins increases steadily, it is necessary to determine how to operate them most effectively and efficiently. In this article, the digital twin synchronization problem is introduced and defined formally. Frequent synchronizations would increase cost and data traffic congestion, whereas infrequent synchronizations would increase the bias of the predictions and yield wrong decisions. This work defines the synchronization problem variants in different contexts. To discuss the problem and its solution, the problem of determining when to synchronize an unreliable production system with its digital twin to minimize the average synchronization and bias costs is formulated and analyzed analytically. The state-independent, state-dependent, and full-information solutions have been determined by using a stochastic model of the system. Solving the synchronization problem using simulation is discussed, and an approximate policy is proposed. Our results show that the performance of the state-dependent policy is close to the optimal solution that can be obtained with full information and significantly better than the performance of the state-independent policy. Furthermore, the approximate periodic state-dependent policy yields near-optimal results. To operate digital twins more effectively, the digital twin synchronization problem must be considered and solved to determine the optimal synchronization policy. [ABSTRACT FROM AUTHOR]

This paper is concerned with quantum stochastic differential equations driven by the fermion field in noncommutative space Lp(풞) for 2≤p<∞$$ 2\le p<\infty $$. First, we investigate the existence and uniqueness of Lp$$ {L}&#x0005E;p $$‐solutions of quantum stochastic differential equations in an infinite time horizon by using the noncommutative Burkholder–Gundy inequality given by Pisier and Xu and the noncommutative generalized Minkowski inequality. Then, we investigate the stability, self‐adjointness, and Markov properties of Lp$$ {L}&#x0005E;p $$‐solutions and analyze the error of numerical schemes of quantum stochastic differential equations. The results of this paper can be utilized for investigating the optimal control of quantum stochastic systems with infinite dimensions. [ABSTRACT FROM AUTHOR]

This article proposes a novel multidimensional Taylor network (MTN)‐based adaptive finite‐time control approach for stochastic nonlinear systems with input saturation constraints. First, by introducing the hyperbolic tangent function, a piecewise smooth function is proposed to approximate the input saturation constraints, which can solve the problem caused by input saturation. Then, with the aid of MTN approximation theorem, a novel adaptive finite‐time control approach is proposed, which can guarantee that all signals of the closed‐loop system are semi‐globally finite‐time stability in probability (SGFTSP), the system output follows the given reference signal, meanwhile, the tracking error converges to a small neighborhood of the origin in finite‐time. Compared with the existing results, the proposed approach has the characteristics of simple structure and low calculation, which can achieve the satisfactory control performance with a reduced computational burden. In the end, the effectiveness of the proposed approach is validated by Lyapunov stability theory and two simulation experiments. [ABSTRACT FROM AUTHOR]

Many practical dynamic models always suffer from complex nonlinearities, parameter uncertainties and random noises. Such kind of models are always characterized by uncertain stochastic nonlinear systems. Besides, many factors will lead to dead‐zone actuator, which further adds more challenges to control engineering. This paper studies stabilization issue of stochastic systems with polynomial nonlinear conditions, unknown parameters and dead‐zone actuator. An adaptive control approach is proposed by exploring homogeneous domination control and using dynamic‐gain‐based adaptive design strategy. It shows that all the signals are bounded almost surely and the system states converge to the origin almost surely. The presented method is successfully applied to the mass spring mechanical system. [ABSTRACT FROM AUTHOR]

In this article, we investigate the input‐to‐state stability (ISS) of stochastic systems via intermittent event‐triggered control. The control update sequence during the control intervals is determined through an event‐triggered mechanism (ETM), where the periodic ETM and continuous ETM are considered separately. For the continuous ETM, a positive minimum inter‐execution time is ensured by adding waiting time, which avoids Zeno behavior. For the periodic ETM, with the help of Halanay‐like inequality, the maximum allowable bound of the sampling period is given. The number of control updates is further reduced by adding a dynamic term. In addition, sufficient conditions for ISS in stochastic systems are proposed by designing an auxiliary timer and applying the Lyapunov method. Finally, two numerical examples are presented to verify the validity of the results. [ABSTRACT FROM AUTHOR]

Background: Antimicrobial resistance (AMR) represents a significant threat to global health with Neisseria gonorrhoea emerging as a key pathogen of concern. In Australia, the Australian Gonococcal Surveillance Program (AGSP) plays a critical role in monitoring resistance patterns. However, antibiotic susceptibility test (AST) uptake – a crucial component for effective resistance surveillance – remains to be a limiting factor. The study aims to model the processes involved in generating AST tests for N. gonorrhoea isolates within the Australian healthcare system and assess the potential impact of systematic and policy-level changes. Methods: Two models were developed. The first model was a mathematical stochastic health systems model (SHSM) and a Bayesian Belief Network (BBN) to simulate the clinician-patient dynamics influencing AST initiation. Key variables were identified through systematic literature review to inform the construction of both models. Scenario analyses were conducted with the modification of model parameters. Results: The SHSM and BBN highlighted clinician education and the use of clinical support tools as effective strategies to improve AST. Scenario analysis further identified adherence to guidelines and changes in patient-level factors, such as persistence of symptoms and high-risk behaviours, as significant determinants. Both models supported the notion of mandated testing to achieve higher AST initiation rates but with considerations necessary regarding practicality, laboratory constraints, and culture failure rate. Conclusion: The study fundamentally demonstrates a novel approach to conceptualising the patient-clinician dynamic within AMR testing utilising a model-based approach. It suggests targeted interventions to educational, support tools, and legislative framework as feasible strategies to improve AST initiation rates. However, the research fundamentally highlights substantial research gaps in the underlying understanding of AMR. [ABSTRACT FROM AUTHOR]

This paper is devoted to analyzing a kind of fractional stochastic neutral system (FSNS). Firstly, by introducing the notion of newly defined two-parameter Mittag-Leffler matrix function, we derive the solution of the corresponding linear stochastic system. Subsequently, for the linear case, by virtue of the Grammian matrix, we give a suffcient and necessary condition to guarantee the relatively exact controllability for the addressed case. Furthermore, for the nonlinear one, the relatively exact controllability is obtained by fixed point and explore it via Banach contraction principle. Finally, two examples are provided to intensify our theoretical conclusions. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the approximate controllability of fractional stochastic Sobolev-type hemivariational differential systems of order r ∈ (1, 2) with sectorial operators. Firstly, by using stochastic analysis, fractional calculus, sine and cosine family operators, sectorial operators, and the fixed-point theorems of multivalued maps, we show the existence of mild solutions for the fractional stochastic evolution systems. Then, we provide a sufficient condition to guarantee the approximate controllability of the stochastic evolution systems. Next, our results cover problems involving nonlocal conditions. Finally, we present theoretical and practical applications to support the validity of the study. [ABSTRACT FROM AUTHOR]

In this investigation, we delve into the dynamics of an ecoepidemic model, considering the intertwined influences of fear, refuge-seeking behavior, and alternative food sources for predators with selective predation. We extend our model to incorporate the impact of fluctuating environmental noise on system dynamics. The deterministic model undergoes thorough scrutiny to ensure the positivity and boundedness of solutions, with equilibria derived and their stability properties meticulously examined. Furthermore, we explore the potential for Hopf bifurcation within the system dynamics. In the stochastic counterpart, we prioritize discussions on the existence of a globally positive solution. Through simulations, we unveil the stabilizing effect of the fear factor on susceptible prey reproduction, juxtaposed against the destabilizing roles of prey refuge behavior and disease prevalence intensity. Notably, when disease prevalence intensity is too low, the infection can be eradicated from the ecosystem. Our deterministic analysis reveals a complex interplay of factors: the system destabilizes initially but then stabilizes as the fear factor suppressing disease prevalence intensifies, or as predators exhibit a stronger preference for infected prey over susceptible ones, or as predators are provided with more alternative food sources. Moreover, for the stochastic system, the oscillations tend to cluster around the coexistence equilibrium of the corresponding deterministic model when white noise intensity is low. However, with increasing white noise intensity, oscillation amplitudes escalate. Critically, very high levels of white noise can lead to the eradication of infection from the ecosystem. [ABSTRACT FROM AUTHOR]

This paper is concerned with the synchronization of stochastic uncertain complex dynamic networks with time‐varying delays. In contrast to existing synchronization network models, the current study considers both internal time‐varying delays and coupling time‐varying delays. By analyzing the two factors (i.e. time‐varying delays and uncertainties) on the synchronization performance of stochastic uncertain complex dynamic networks, a new inverse optimal adaptive control is proposed. The analysis tool developed in this paper is based on Lyapunov technique, algebraic graph theory and inverse optimality, which does not need to solve Hamilton‐Jacobi‐Bellman equation. Some sufficient conditions are established for the synchronization of stochastic uncertain complex dynamic networks with time‐varying delays. To demonstrate the effectiveness of the present approach, simulation results are illustrated. In this paper, we consider the synchronization of stochastic uncertain complex dynamic networks with time‐varying delays. Different from the existing synchronization of the networks model, we take the internal time‐varying delays and the coupling time‐varying delays into account. By analyzing the two factors (i.e. time‐varying delays and uncertainties) on the synchronization performance of stochastic uncertain complex dynamic networks, a novel inverse optimal adaptive control is proposed. The analysis tool developed in this paper is based on Lyapunov technique, algebraic graph theory and inverse optimality, which does not need to solve Hamilton‐Jacobi‐Bellman equation. Some sufficient conditions are established for the synchronization of stochastic uncertain complex dynamic networks with time‐varying delays. [ABSTRACT FROM AUTHOR]

Fractional differential equations, which are non-local and can better describe memory and genetic properties, are widely used to describe various physical, chemical, and biological phenomena. Therefore, the multi-agent systems based on discrete-time fractional stochastic models are established. First, some followers are selected for pinning control. In order to save resources and energy, an event-triggered based control mechanism is proposed. Second, under this control mechanism, sufficient conditions on the interaction graph and the fractional derivative order such that formation control can be achieved are given. Additionally, influenced by noise, the multi-agent system completes formation control in the mean square. In addition to that, these results are equally applicable to the discrete-time fractional formation problem without noise. Finally, the example of numerical simulation is given to prove the correctness of the results. [ABSTRACT FROM AUTHOR]

This paper extends a kinetic-potential energy shaping method to stochastic mechanical port-Hamiltonian systems. The kinetic-potential energy shaping brings a new class of Lyapunov function candidates involving a cross term of the position and the momentum without solving partial differential equations for deterministic port-Hamiltonian systems. However, the conventional kinetic-potential energy shaping does not necessarily work for stochastic port-Hamiltonian systems due to energy increase by stochastic noise. Therefore, we first provide a modification properly compensated by using stochastic generalized canonical transformations. Then, two stochastic stability results are presented. The first result shows a necessary condition for stochastic asymptotic stability for an equilibrium state. The other one shows a necessary condition for stochastic bounded stability for a target state, which is not necessarily an equilibrium point. [ABSTRACT FROM AUTHOR]

This paper investigates the adaptive control for a class of constrained stochastic nonlinear systems with parametric uncertainty and input saturation. Based on a novel radial basis function neural networks (RBF NNs), the nonlinearities are tackled without the prior knowledge of NN nodes and weights. The approximate coordinate coordination is combined with an auxiliary system to attenuate the effects generated by input saturation. Then, an opportune backstepping design procedure is presented using the barrier Lyapunov function (BLF) and RBF NN. Based on this design procedure, an adaptive state–feedback controller is constructed, which makes the closed-loop system semi-globally uniformly ultimately bounded, the tracking error bounded in a compact set of the origin, and the full-states not violated. Finally, a stochastic single-link robot arm system is simulated to demonstrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

The H ∞ control problem is studied for discrete-time Markov jump systems with both discrete and distributed delays. The controller to be designed allows for mode mismatch with the plant, and the mode mismatch behavior is described by a hidden Markov model. The conditional probabilities are permitted to be uncertain, which belong to an interval with precise upper and lower bounds. A sufficient condition that ensures the stochastic stability and H ∞ disturbance-attenuation performance of the system is derived by employing a Lyapunov functional involving multiple quadratic items associated with the system modes. Then, two design methods are proposed for the desired controller. The first method does not utilize the property that the row sum of the conditional probability matrix is one, while the second method incorporates this property into the design process. The scenario where all the conditional probabilities are known in advance is also investigated, and corresponding controller design methods are presented. Finally, two examples are applied to validate the effectiveness of the design methods. [ABSTRACT FROM AUTHOR]

This paper is concerned with the exponential contraction and expansion of regime-switching diffusions. The focus is on the behavior of the distance from one solution to another solution, rather than with respect to some equilibrium point. The moment and almost sure exponential contraction and expansion are investigated. General criteria and easily verifiable conditions for the moment and almost sure exponential contraction and expansion are obtained. The contribution of the Markovian switching to the exponential contraction and expansion is revealed. Several examples together with numerical experiments are provided for demonstration. The convergence of contracting observers with noisy measurements under Markovian switching and the connection between exponential contraction and global attractivity of stochastic population systems are presented. [ABSTRACT FROM AUTHOR]

This paper investigates the adaptive neural tracking control problem for a class of stochastic nonlinear systems with time delays and full-state constraints in a unified framework for the first time. The time-delay terms of the controlled systems are compensated by novel Lyapunov–Krasovskii functionals. The asymmetric barrier Lyapunov function (BLF) is adopted to guarantee that the full states are always restricted within prescribed constraints. RBF neural networks are utilised to approximate the lumped unknown functions in the design process. Furthermore, the dynamic surface control (DSC) technique is employed to simplify the process of control design significantly. Stability analysis shows all closed-loop signals are SGUUB, and full-state constraints are not violated. Finally, simulation results confirm the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper addresses the output feedback adaptive resilient control problem for a class of stochastic nonlinear systems under sensor and actuator attacks. By applying a linear state transformation, the original system is transformed into a new one for which output feedback control becomes possible. The Nussbaum function is exploited to overcome the unknown control direction problem generated by uncertain control coefficients and adversary attacks. Based on the available compromised output signal and the states reconstructed by a new extended state observer, an output feedback adaptive resilient control scheme is proposed for such systems by combining the neural-networks-based approximation approach, backstepping technique and some special methods. The proposed controller can guarantee that all signals in the closed-loop system are semiglobally bounded in probability and the stabilisation error variables remain in an adjustable vicinity of origin. Finally, the effectiveness and applicability of the proposed control methodology is verified by two illustrative examples. [ABSTRACT FROM AUTHOR]

From the perspective of accuracy, efficiency and versatility, calculating statistical moments for different forms of performance functions in a unified way remains a challenge, and their accuracy also considerably affects the results of subsequent reliability analysis. In this article, a new dimension-reduction model, termed as adaptive hybrid dimension-reduction model (AH-DRM), is derived to approximate the performance functions with different characteristics relatively accurately. Based on the AH-DRM, a highly flexible point estimation method (PEM), which has good versatility for the various forms of performance function, is developed for statistical moments estimation of stochastic systems. Subsequently, to illustrate the performance of the proposed method for different performance function forms, three examples, including weakly, moderately and strongly nonlinear benchmark examples, are investigated. The results indicate that the proposed method is versatile for each example and can receive desirable accuracy for evaluating the first-four central moments of the performance functions with high efficiency. Finally, the developed PEM is applied to reconstruct the probability density function of the performance function and calculate the reliability of structures with the aid of the saddlepoint approximation (SPA) method, and two practical engineering examples are used to verify the applicability of the proposed method in structural reliability analysis. [ABSTRACT FROM AUTHOR]

As a key component of rotating machinery, it is of great significance for the timely diagnosis of bearing weak faults. Stochastic resonance is widely used for its special signal enhancement pattern, and the combination of system parameters determines its actual output effect. Because the social mimic optimization algorithm has the advantages of few parameters, fast convergence speed and strong exploitation capability, it is used to optimize the parameters of stochastic resonance system in this paper. Aiming at the problem that it is easy to fall into local optimum during optimization, inspired by the learning habits of elite, an elite social mimic optimization (ESMO) algorithm is proposed. Its improvement mainly includes five parts: integration of learning efficiency, exchange learning, looking for successors, innovation and breakthrough, elimination mechanism. And its superiority is verified by the comparison of 29 standard benchmark functions and 10 other well-known optimization algorithms. Aiming at the discontinuity of optimization space, the concept of survival rate (surr) is proposed, and the effectiveness of the ESMO algorithm in optimizing discontinuous variables is analyzed and verified. Aiming at the disadvantage that stochastic resonance can only process small frequency signals, a bearing weak fault diagnosis method based on frequency exchange and parameter compensation stochastic resonance is proposed. To verify its application ability in other fault diagnosis methods, a classification and recognition method based on BP neural network is proposed. Finally, the effectiveness and superiority of the ESMO algorithm are verified by simulation signals and bearing experimental data. The above analysis results prove that the ESMO algorithm has certain scientific and engineering application value in the optimization field and engineering application. [ABSTRACT FROM AUTHOR]

To monitor the dynamic behavior of degrading systems over time, a flexible hierarchical discrete-time state-space model (SSM) is introduced that can mathematically characterize the stochastic evolution of the latent states (discrete, continuous, or hybrid) of degrading systems, dynamic measurements collected from condition monitoring sources (e.g., sensors with mixed-type outputs), and the failure process. This flexible SSM is inspired by Bayesian hierarchical modeling and recurrent neural networks without imposing prior knowledge regarding the stochastic structure of the system dynamics and its variables. The temporal behavior of degrading systems and the relationship between variables of the corresponding system dynamics are fully characterized by stochastic neural networks without having to define parametric relationships/distributions between deterministic and stochastic variables. A Bayesian filtering-based learning method is introduced to train the structure of the proposed framework with historical data. Also, the steps to utilize the proposed framework for inference and prediction of the latent states and sensor outputs are discussed. Numerical experiments are provided to demonstrate the application of the proposed framework for degradation system modeling and monitoring. [ABSTRACT FROM AUTHOR]

The stochastic P-bifurcation behavior of bi-stability in a generalized van der Pol oscillator with the fractional damping under colored noise and thermal excitation is investigated. Firstly, using the principle of minimal mean square error and linearization method, the non-linear stiffness terms can be equivalent to a linear stiffness which is a function of the system amplitude, and the original system is simplified to an equivalent integer order van der Pol system. Secondly, the system amplitude stationary probability density function is obtained by the stochastic averaging, and then based on the singularity theory, the critical parametric conditions for the system amplitude stochastic P-bifurcation are found. Finally, the types of the stationary probability density function of the system amplitude are qualitatively analyzed in each area divided by the transition set curves. The consistency between the analytical results and the numerical results acquired from Monte-Carlo simulation also testifies the theoretical analysis in this paper and the method used in this paper can directly guide the design of the fractional order controller to adjust the response of the system. [ABSTRACT FROM AUTHOR]

In this paper, the H∞$$ {H}_{\infty } $$ saturated control problems of networked systems with random sampling periods and stochastic transmission delays are investigated. The main issue is to design an H∞$$ {H}_{\infty } $$ saturated controller such that the controlled close‐loop system is exponentially mean‐square stable with a desired H∞$$ {H}_{\infty } $$ performance. A matrix exponential which is different from some existing literature is used to reconstruct the discrete‐time stochastic system to an equivalent yet tractable augmented model without any additional conditional constraint. In virtue of reduced‐order confluent Vandermonde matrix approach and Kronecker product operation, the stability condition in terms of linear matrix inequality is derived and then the desired H∞$$ {H}_{\infty } $$ saturated controller is designed. It should be emphasized that the improved method can also be used for the stability analysis and controller design when the system matrix contains complex roots. Finally, two numerical examples and a three‐axis milling machine system are utilized to manifest the reliability and practicality of the designed strategy. [ABSTRACT FROM AUTHOR]

We investigate a stochastic version of the Allen–Cahn–Navier–Stokes system in a smooth two- or three-dimensional domain with random initial data. The system consists of a Navier–Stokes equation coupled with a convective Allen–Cahn equation, with two independent sources of randomness given by general multiplicative-type Wiener noises. In particular, the Allen–Cahn equation is characterized by a singular potential of logarithmic type as prescribed by the classical thermodynamical derivation of the model. The problem is endowed with a no-slip boundary condition for the (volume averaged) velocity field, as well as a homogeneous Neumann condition for the order parameter. We first prove the existence of analytically weak martingale solutions in two and three spatial dimensions. Then, in two dimensions, we also establish pathwise uniqueness and the existence of a unique probabilistically-strong solution. Eventually, by exploiting a suitable generalisation of the classical De Rham theorem to stochastic processes, existence and uniqueness of a pressure is also shown. [ABSTRACT FROM AUTHOR]

A wide range of phenomena in the natural and social sciences involve large systems of interacting particles, including plasmas, collections of galaxies, coupled oscillators, cell aggregations, and economic "agents." Kinetic methods for reducing the complexity of such systems typically involve the derivation of nonlinear partial differential equations for the corresponding global densities. In recent years, there has been considerable interest in the mean field limit of interacting particle systems with long-range interactions. Two major examples are interacting Brownian particles in the overdamped regime and the Kuramoto model of coupled phase oscillators. In this paper, we analyze these systems in the presence of local or global stochastic resetting, where the position or phase of each particle independently or simultaneously resets to its original value at a random sequence of times generated by a Poisson process. In each case, we derive the Dean–Kawasaki (DK) equation describing hydrodynamic fluctuations of the global density and then use a mean field ansatz to obtain the corresponding nonlinear McKean–Vlasov (MV) equation in the thermodynamic limit. In particular, we show how the MV equation for global resetting is driven by a Poisson noise process, reflecting the fact that resetting is common to all of the particles and, thus, induces correlations that cannot be eliminated by taking a mean field limit. We then investigate the effects of local and global resetting on nonequilibrium stationary solutions of the macroscopic dynamics and, in the case of the Kuramoto model, the reduced dynamics on the Ott–Antonsen manifold. [ABSTRACT FROM AUTHOR]

Black-box systems are inherently hard to verify. Many verification techniques, like model checking, require formal models as a basis. However, such models often do not exist, or they might be outdated. Active automata learning helps to address this issue by offering to automatically infer formal models from system interactions. Hence, automata learning has been receiving much attention in the verification community in recent years. This led to various efficiency improvements, paving the way toward industrial applications. Most research, however, has been focusing on deterministic systems. In this article, we present an approach to efficiently learn models of stochastic reactive systems. Our approach adapts L ∗ -based learning for Markov decision processes, which we improve and extend to stochastic Mealy machines. When compared with previous work, our evaluation demonstrates that the proposed optimizations and adaptations to stochastic Mealy machines can reduce learning costs by an order of magnitude while improving the accuracy of learned models. [ABSTRACT FROM AUTHOR]

This paper introduces a multidisciplinary conceptual perspective encompassing artificial intelligence (AI), artificial general intelligence (AGI), and cybernetics, framed within what we call the formalism of generalized neuromorphism. Drawing from recent advancements in computing, such as neuromorphic computing and spiking neural networks, as well as principles from the theory of open dynamical systems and stochastic classical and quantum dynamics, this formalism is tailored to model generic networks comprising abstract processing events. A pivotal aspect of our approach is the incorporation of the memory space and the intrinsic non-Markovian nature of the abstract generalized neuromorphic system. We envision future computations taking place within an expanded space (memory space) and leveraging memory states. Positioned at a high abstract level, generalized neuromorphism facilitates multidisciplinary applications across various approaches within the AI community. [ABSTRACT FROM AUTHOR]

In this paper, we unite concepts from Husserlian phenomenology, the active inference framework in theoretical biology, and category theory in mathematics to develop a comprehensive framework for understanding social action premised on shared goals. We begin with an overview of Husserlian phenomenology, focusing on aspects of inner time-consciousness, namely, retention, primal impression, and protention. We then review active inference as a formal approach to modeling agent behavior based on variational (approximate Bayesian) inference. Expanding upon Husserl's model of time consciousness, we consider collective goal-directed behavior, emphasizing shared protentions among agents and their connection to the shared generative models of active inference. This integrated framework aims to formalize shared goals in terms of shared protentions, and thereby shed light on the emergence of group intentionality. Building on this foundation, we incorporate mathematical tools from category theory, in particular, sheaf and topos theory, to furnish a mathematical image of individual and group interactions within a stochastic environment. Specifically, we employ morphisms between polynomial representations of individual agent models, allowing predictions not only of their own behaviors but also those of other agents and environmental responses. Sheaf and topos theory facilitates the construction of coherent agent worldviews and provides a way of representing consensus or shared understanding. We explore the emergence of shared protentions, bridging the phenomenology of temporal structure, multi-agent active inference systems, and category theory. Shared protentions are highlighted as pivotal for coordination and achieving common objectives. We conclude by acknowledging the intricacies stemming from stochastic systems and uncertainties in realizing shared goals. [ABSTRACT FROM AUTHOR]

Stochastic reaction networks are widely used in the modeling of stochastic systems across diverse domains such as biology, chemistry, physics, and ecology. However, the comprehension of the dynamic behaviors inherent in stochastic reaction networks is a formidable undertaking, primarily due to the exponential growth in the number of possible states or trajectories as the state space dimension increases. In this study, we introduce a knowledge distillation method based on reinforcement learning principles, aimed at compressing the dynamical knowledge encoded in stochastic reaction networks into a singular neural network construct. The trained neural network possesses the capability to accurately predict the state conditional joint probability distribution that corresponds to the given query contexts, when prompted with rate parameters, initial conditions, and time values. This obviates the need to track the dynamical process, enabling the direct estimation of normalized state and trajectory probabilities, without necessitating the integration over the complete state space. By applying our method to representative examples, we have observed a high degree of accuracy in both multimodal and high-dimensional systems. Additionally, the trained neural network can serve as a foundational model for developing efficient algorithms for parameter inference and trajectory ensemble generation. These results collectively underscore the efficacy of our approach as a universal means of distilling knowledge from stochastic reaction networks. Importantly, our methodology also spotlights the potential utility in harnessing a singular, pretrained, large-scale model to encapsulate the solution space underpinning a wide spectrum of stochastic dynamical systems. [ABSTRACT FROM AUTHOR]

In order to solve continuous stochastic Lyapunov equations, a novel implicit iterative algorithm is presented by means of successive over relaxation (SOR) iteration in this article. Throughout this method, three tuning parameters are added for the improvement of the convergence rate. It is shown that this algorithm is monotonically bounded, and the convergence condition is also given and extended. Applying the latest updated estimates, this algorithm can attain a better convergence performance compared with other existing iterative algorithms when choosing appropriate tuning parameters. Finally, a numerical example is provided to illustrate the feasibility and priority of this approach. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of parameter identification for discrete-time stochastic systems with unknown exogenous inputs. These systems form an important class of dynamic stochastic system models used to describe objects and processes under a high level of a priori uncertainty, when it is not possible to make any assumptions about the evolution of the unknown input signal or its statistical properties. The main purpose of this paper is to construct a new SVD-based modification of the existing Gillijns and De Moor filtering algorithm for linear discrete-time stochastic systems with unknown exogenous inputs. Using the theoretical results obtained, we demonstrate how this modified algorithm can be applied to solve the problem of parameter identification. The results of our numerical experiments conducted in MATLAB confirm the effectiveness of the SVD-based parameter identification method that was developed, under conditions of unknown exogenous inputs, compared to maximum likelihood parameter identification when exogenous inputs are known. [ABSTRACT FROM AUTHOR]

Summary: By using the collected batch data and the iterative search, and based on the filtering identification idea, this article investigates and proposes a filtered multi‐innovation generalized projection‐based iterative identification method, a filtered generalized gradient‐based iterative identification method, a filtered generalized least squares‐based iterative identification method, a filtered multi‐innovation generalized gradient‐based iterative identification method and a filtered multi‐innovation generalized least squares‐based iterative identification method for equation‐error autoregressive systems described by the equation‐error autoregressive models. These filtered generalized iterative identification methods can be extended to other linear and nonlinear scalar and multivariable stochastic systems with colored noises. [ABSTRACT FROM AUTHOR]

This paper aims to derive a new set of sufficient conditions for the existence and approximate controllability of neutral‐type fractional stochastic integrodifferential inclusions with infinite delay and non‐instantaneous impulse in a separable Hilbert space using the Atangana–Baleanu Caputo fractional derivative. We investigate the existence of a mild solution for the Atangana–Baleanu Caputo fractional neutral‐type delay integrodifferential stochastic system while taking into account the non‐instantaneous impulses. For this purpose, the Atangana–Baleanu Caputo fractional neutral‐type impulsive delay stochastic system is transferred into an equivalent fixed point problem via an integral operator, and then, the Bohnenblust–Karlin fixed point approach is applied. Further, the approximate controllability results of the proposed nonlinear stochastic impulsive control system are established under the consideration that the corresponding linear system is approximately controllable. The set of sufficient conditions is established by using the concepts of stochastic analysis, fractional calculus, fixed point technique, semigroup theory of bounded linear operators, and the theory of multivalued maps. To illustrate the abstract results, we provide an example at the end of the paper. [ABSTRACT FROM AUTHOR]

The impulsive effect on the fractional stochastic integrodifferential system of order ϱ∈(1,2)$$ \varrho \in \left(1,2\right) $$ with infinite delay via sectorial operator is investigated in this work. The primary findings of this study are tested by referring to multivalued functions, sectorial operators, fractional derivatives, and the fixed point approach. Initially, the presence of a mild solution for the systems class was introduced. The existence outcomes of semilinear control problems were then established. Eventually, an application is given for deriving the theory of the key findings. [ABSTRACT FROM AUTHOR]

In the context of "dual carbon" objectives, ESG investment concept has received wide attention. In this paper, based on stochastic systems and stakeholder theory, we analyze the interest requirements of subject stakeholders and investigate the agency conflict and coordination problems in the system. Combining with the contract theory, we construct a continuous-time principal-agent model with ambiguity aversion under ESG rating Knightian uncertainty. By the method of stochastic calculus in multiple priors, we derive the HJB equation for the optimal dynamic contract value function based on ESG rating Knightian uncertainty under incentive compatibility conditions. Then, for different ESG rating levels, through numerical simulation, we discuss the impact of the Knightian uncertainty degree of ESG rating on the optimal contract. The study shows that as the Knightian uncertainty degree of ESG rating increases, companies are more inclined to green development and the maximum expected return of principals decreases. [ABSTRACT FROM AUTHOR]

In this paper, the control issue of adaptive fault-tolerant is studied for a class of stochastic nonlinear systems with multiple faults and full state constraints, with multiple faults including the actuator faults and the external system fault. The problem with full state constraints are solved by constructing a logarithmic barrier Lyapunov functions (BLFs). By integrating multi-dimensional Taylor network (MTN) technology into the backstepping process, a new adaptive MTN-based fault-tolerant controller is designed. On the basis of considering multiple faults, the proposed control strategy can ensure that all signals in the closed-loop system are semi-global ultimately uniformly bounded (SGUUB) in probability, and all states of the system are constrained within the given boundary. Finally, three simulation examples are given to illustrate the effectiveness and practicability of the proposed control strategy. [ABSTRACT FROM AUTHOR]

This paper investigates the non-fragile robust H ∞ control problem of nonlinear uncertain neutral stochastic Takagi–Sugeno (T–S) fuzzy systems with mixed time-delays. The uncertainties are norm-bounded and time-varying. Sufficient conditions for H ∞ performance analysis results of the delay-dependent condition is established via the Lyapunov–Krasovskii functional (LKF) technique and linear matrix inequality (LMI) method. Based on the H ∞ performance result, a desired fuzzy control is designed by solving LMIs. Finally, an example is provided to illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This article presents an annular finite-time H ∞ filtering approach for continuous-time mean-field stochastic systems (MFSSs). Our attention is focused on obtaining a set of stability criteria for analyzing the H ∞ performance and the annular finite-time boundedness of the filtering error system. Sufficient conditions in the form of linear matrix inequality (LMI) are established to guarantee the existence of the designed filter. Then, the filter gains are derived through a convex optimization problem. Through a simulation example, the validity of the obtained results is demonstrated. [ABSTRACT FROM AUTHOR]

• A chat service with actively involved customers and repeating interactions is studied. • The capacity of parallel chats and the server's response effort are derived. • A queueing game for a dual-channel system of chat service and call center is analyzed. • Customer bounded rationality is considered. Many service systems in various type of industry provide services via chat technologies. This type of service system is characterized by an interesting combination of properties. First, the customer is actively involved in service execution, since the service is comprised of responses of the server and the customer to each other, until the customer's request is satisfied. In addition, in such a system, the service can be provided by a single server in a parallel manner to a number of customers. Motivated by these and others interesting properties of the chat service, we formulate and analyze the stochastic queueing system as a two-dimensional quasi-birth-and-death process and derive its steady-state probabilities using matrix geometric methods. By means of economic analysis, we provide a scheme for deriving the optimal capacity of parallel chats and the optimal response effort that should be made by the server, considering that higher effort lengthens the response time but increases the probability of successful service completion. We next investigate a queueing game that considers a multi-channel service system consisting of a chat service and a traditional multi-server call center, and we consider strategic customers under both a centralized and a decentralized scenario. We show that competition between service channels may lead to lower service utilization even though customers enjoy higher expected utility. Finally, customer bounded rationality is considered and it is shown that customers who are less rational may enjoy higher utility. Sensitivity analyses are conducted for all scenarios. [ABSTRACT FROM AUTHOR]