This paper examines a fractional-order prey–predator system in the context of alien species invasion, where the food chain consists of prey, an intermediate predator, and an invasive top predator. The model incorporates fear effects, prey refuge, and the Sokol–Howell functional response to capture ecological realism. We first prove the existence, uniqueness, and boundedness of solutions. Then, we conduct a local and global stability analysis of the system’s equilibrium points, deriving sufficient conditions for stability. We then apply Pontryagin’s maximum principle to derive the optimal control of the system and discuss the existence of the corresponding optimal solution. Finally, we conduct numerical simulations under different fractional orders to analyze the dynamic responses of all species, comparing cases with and without optimal control. The outcomes show that optimal control can efficiently stabilize population dynamics, and that the fractional order considerably affects the convergence rate to reach the equilibrium. These findings provide theoretical insights and methodological tools for maintaining ecosystem stability, protecting biodiversity, and mitigating the ecological risks posed by invasive species.

Optimal energy management of heterogeneous consumer electronics in IoT microgrids is challenged by the need to aggregate sensitive device parameters in centralized scheduling and physical-time sluggishness in synchronous distributed solvers. This paper proposes an asynchronous alternating direction method of multipliers framework for distributed power scheduling. We develop a convex model that transforms device constraints into quadratic costs. A delay-aware asynchronous update scheme with random node wake-up is designed, providing an O(1) closed-form projection for capability-constrained edge nodes and formulating energy storage as a quadratic programming. To handle errors from asynchronous delays, a novel Lyapunov function with arithmetic progression on historical states is introduced, establishing a theoretical bound between permissible delays and algorithm parameters.

In this article, the large-time asymptotic wave dynamics of rogue curves are analytically investigated and numerically confirmed in the Davey-Stewartson (DS) I equation. We show that, when time in bilinear expressions of the rogue curves is large, a certain number of localized lump-shaped waves would arise on the uniform background, exhibiting various wave patterns. We further show that, as time increases, the individual lump-shaped wave asymptotically evolves into a line soliton on the constant background that persist at large time. By performing large-time asymptotic analysis, we reveal that such wave patterns as well as the numbers of lump-shaped waves can be analytically determined by the structure of nonzero roots of the Wronskian-Hermite polynomials. Our asymptotic predictions are compared to true solutions quantitatively and excellent agreement is obtained.

This paper studied a problem of prescribed-time control for biological systems with invasive species. A new prescribed-time stability theorem was proposed within the framework of adaptive control. Utilizing this theorem, a novel state feedback control strategy was designed using the backstepping method for biological systems with unknown parameters, ensuring convergence within a prescribed time. A noval feature of the proposed controller was its continuous time-varying feedback structure, which guaranteed that all system states converged to a stable equilibrium point within the prescribed time. Importantly, the prescribed time was independent of initial conditions and could be adjusted arbitrarily within physical constraints, thus offering significant flexibility in practical applications. To verify the effectiveness of the proposed algorithm, corresponding simulation experiments were provided in this paper, demonstrating its robustness and efficiency in achieving the desired control objectives. This work not only advanced the theoretical foundation of prescribed-time control but also provided practical solutions for managing biological systems threatened by invasive species.

This paper analyzes a reaction-diffusion SIS model with spatial heterogeneity using singular perturbation theory and the method of asymptotic matching. By introducing small parameters and nondimensionalization, a reaction-diffusion singular perturbation system with fast-slow time scale structure is constructed. Unlike previous studies, this paper constructs both internal and external solutions that describe the early-phase changes and long-term equilibrium of the disease on the fast and slow time scales, and achieves smooth matching through matching conditions to obtain a composite asymptotic solution. Next, the validity and high-order convergence of this solution are proved. Finally, the system is discretized in space and time using the IMEX numerical method, and the results validate the layered dynamic features of susceptible and infected individuals. Further numerical simulations show that the composite asymptotic solution agrees highly with the numerical solution, confirming the correctness and stability of the method. This study provides a new theoretical framework and numerical method for the dynamical analysis of multi-scale reaction-diffusion systems in infectious disease modeling.

Aiming at the problems of random disturbances, unknown nonlinear terms, and control resource consumption in biological systems invaded by alien species, the present study proposes a control strategy that fuses the Generalized Fuzzy Hyperbolic Model (GFHM) with the event-triggered mechanism. First, the GFHM is employed to substitute for the conventional Fuzzy Logic System (FLS) in approximating the system’s unknown nonlinear terms, and its structural advantage based on hyperbolic tangent functions is utilized to improve approximation accuracy. Secondly, an appropriate controller is designed via the backstepping method. In order to cut down on superfluous control signal transmission and decrease communication costs, an event-triggered mechanism is incorporated into the controller design, while the actual control input is updated discretely only when the predefined error threshold is surpassed. Theoretical investigations demonstrate that the proposed strategy can guarantee all system states maintain semi-global uniform ultimate boundedness, while the tracking error of native species density converges toward a small neighborhood around zero. In simulation experiments, the invasion of Hypostomus plecostomus is taken as an example, and the superiority of the proposed method in control accuracy is verified.

Extracting dynamic, uncertain, and multimode features of process data is important and challenging for fault diagnosis. However, the traditional fault diagnosis methods mainly focus on a single feature extraction, and there are few fault diagnosis methods that can extract multimode features. In this paper, a new fault detection and classification method based on augmented switching linear dynamic latent variable (ASLDLV) model are proposed, which can solve the problem of multimode feature extraction, and mine dynamic, uncertain and multimode features simultaneously in process modeling for fault detection and classification. First, a linear dynamic latent variable (LDLV) model is introduced to extract the dynamic and uncertain of process samples. Furthermore, an augmented dynamic switching transition matrix is embedded in LDLV model to describe multiple modes characteristics. In this way, an augmented dynamic switching transition matrix can be used to mine deeper dynamic correlation between multiple modes so that the ASLDLV model is achieved. The proposed ASLDLV model not only can consider the dynamics, uncertain and multimode characteristics of data at the same time, but also it is better to represent dynamic relationship of multiple models so that a more accurate switching model is determined. Finally, the ASLDLV model is applied to Tennessee Eastman process for fault detection and classification, compared with some exiting methods. The simulation results illustrate the effectiveness and superiority of ASLDLV model.

This paper establishes a new stochastic SIR epidemic model that incorporates telegraph noise and Lévy noise to simulate the complex environmental disturbances affecting disease transmission. Given the susceptibility of epidemic spread to environmental noise and its intricate dynamics, an adaptive sliding mode controller based on an integral sliding surface and an adaptive control law is proposed. This controller is capable of stabilizing the constructed model and effectively suppressing the spread of the disease. The main contributions of this paper include the following: establishing a comprehensive and realistic stochastic SIR model that accounts for the complex impacts of telegraph noise (symbolizing periodic environmental changes) and Lévy noise (representing sudden environmental shocks) on the dynamics of disease transmission; employing T-S fuzzy modeling, which considers the design of fuzzy rules and the symmetry of membership functions, to ensure linearization of the model; constructing an integral sliding surface and designing an adaptive sliding mode controller for the fuzzy-processed model. Finally, the effectiveness of the proposed control method is validated through numerical simulations.

. In this paper, for a class of SIR models with saturated incidence, the SIR model is discretized using the modified Euler method to form a form in which the coefficient matrix contains unknown parameters. The augmented error system method is constructed and the future information is simulated as a feed-forward and compensated into the SIR model, and the output regulation method of the linear discrete system is used to design the non-singular terminal sliding mode surface and the exponential convergence law, and the suitable performance index is given to obtain the optimal sliding mode preview controller. Finally, numerical simulation is utilized to verify the effectiveness of the theory and methodology of this paper.

Microplastics (MPs) are increasingly recognized as hotspots for antibiotic resistance genes (ARGs), yet the combined effects of polymer type and particle size on ARG dynamics in the soil plastisphere remain unclear. Here, we employed metagenomic assembly and binning to explore how MP polymer type and particle size jointly modulate ARG carrying frequencies (ACFs), mobility, and microbial hosts with polyethylene (PE), polystyrene (PS), and biodegradable polybutylene succinate (PBS) MPs across a size gradient (1000, 500, and 106 μm). PBS, PS, and PE plastispheres exhibited different size-related trends in ARG association, with PBS showing the strongest and most consistent decline in ACFs. Only PBS showed a corresponding reduction in ARG-MGE co-localization, suggesting size-dependent constraints on horizontal gene transfer. Distinct ARG combinations in ARG-Carrying Contigs (ACCs) also showed plastic-type selectivity, with complex resistance clusters absent in 106 μm PBS samples, potentially due to environmental constraints that limit the assembly or persistence of multigene resistance structures. Potential pathogens Enterobacter bugandensis and Stutzerimonas urumqiensis were markedly reduced in 106 μm PBS samples, a pattern not observed in PS or PE. Bacterial community analysis revealed that smaller PBS particles were associated with reduced richness, increased evenness, and more competitive interactions within co-occurrence networks. These features, together with the decline in ARG abundance and mobility, suggest that enhanced ecological filtering may occur in smaller biodegradable plastispheres, jointly limiting the persistence of resistance genes and their bacterial hosts. Together, our findings highlight the importance of considering both MP type and particle size in assessing plastisphere-associated ARG risks.

. This study investigates an SEIR model constructed to describe directly transmitted infectious diseases caused by bacteria, viruses, or fungi, using the method of matched asymptotic expansions from singular perturbation theory. By introducing a small parameter, dimensionless variables, and a rescaled time variable, the model is reformulated into a singularly perturbed system with an explicit fast-slow variable structure. In contrast to previous studies that primarily focus on steady-state behavior or simplified models, this work systematically constructs inner and outer solutions corresponding to the and late stage (reduced system). Using matching conditions, a power series representation of the asymptotic solution is derived, capturing the dynamic evolution governed by fast and slow variables. Furthermore, with the aid of an auxiliary function and the comparison theorem for differential equations, the uniform validity of the solution within the small parameter regime is rigorously established. Numerical simulations demonstrate that the constructed first-order asymptotic solution maintains high accuracy across all stages of disease transmission, with particularly close agreement with numerical solutions in the middle and late stages. This research not only enhances the analytical tractability of the SEIR model but also provides a robust theoretical framework and methodological support for more complex epidemic models, highlighting the theoretical advantages and methodological innovations of the matched asymptotic method in practical applications.

In this article, a fixed-time algorithm with input limitations are proposed for uncertainty nonlinear systems by utilizing reinforcement learning (RL) and silding mode techniques. Radial basis function (RBF) neural network (NN) is used to implement the designed RL control algorithm. The critic NN and action NN are designed to approximate cost functions and control inputs, respectively. The fixed-time stability can be guaranteed for uncertain systems by utilizing the nonlinear fast terminal silding mode technology. Finally, the Lyapunov candidate function is used to analyze the closed-loop system's stability. Additionally, the time-based convergence of the closedloop system is demonstrated. The effectiveness and superiority of the proposed control law are verified through simulation.

In this article, we report new rogue wave patterns in the (1 + 1)-dimensional three-wave resonant interaction system. These new wave patterns include double trapezoid-shaped structures, nested-double-square structures, and many others, which are formed by individual fundamental rogue waves. These patterns appear when the tau-functions of rogue wave solutions are determinants of Schur polynomials with index jumps of three, and multiple internal parameters in rogue solutions are large and of the single-power form. Analytically, we reveal that these new patterns are determined asymptotically by root structures of multi-parametric generalized Okamoto polynomials, which contain free complex parameters and thus are natural generalizations of the Okamoto-hierarchy polynomials. As a consequence, these multi-parametric rogue patterns are much more diverse than previous rogue patterns associated with the Okamoto-hierarchy polynomials, and their shapes are strongly deformed from multi-parametric generalized Okamoto root structures. Our asymptotic predictions are compared to true rogue solutions quantitatively, and excellent agreement between them is observed.

The growing integration of renewable energy sources, especially photovoltaic (PV) systems, plays a vital role in enhancing energy efficiency and promoting sustainability. However, due to their high dependence on weather conditions, PV systems often exhibit significant intermittency and unpredictability, which complicates power system monitoring, control, and overall stability. To address these issues and strengthen situational awareness as well as operational reliability in PV-integrated grids, accurate and real-time Dynamic State Estimation (DSE) has become increasingly critical. In this paper, we propose the application of the Cubature Kalman Filter (CKF) for DSE in PV systems. The CKF offers a powerful nonlinear filtering framework, which is capable of accurately estimating the internal dynamic states of the PV systems. The simulation results demonstrate that the proposed CKF-based DSE approach effectively tracks the dynamic states of the PV system, thereby contributing to the improved accuracy of state estimation of the PV system.

This paper proposes an adaptive sliding mode control algorithm based on an event-triggered method for first-order linear systems with disturbance. Sliding mode control is introduced to enhance the robustness of the system, and the event-triggered mechanism adopts a triggering threshold related to sliding mode to improve control accuracy. Then, an adaptive law with a dual-layer nested scheme for the control gain is introduced to reduce the chattering effect in the controller. Compared with the existing method, the gain is adjusted in real-time according to the external disturbance, and there is no need to know the priori information of the disturbance derivative in advance. The advantages of the adaptive law based on event-triggered sliding mode control include reducing the communication bandwidth and resource consumption, and the adaptive change of gain can offset the negative effects caused by disturbance more flexibly and suppress the chattering effect effectively. Furthermore, the boundedness of system trajectory and uniform positive lower bound of inter-event time is guaranteed. Finally, two simulation experiments are used to verify the availability and effectiveness of the proposed method.

In this paper, a lattice Boltzmann method is proposed for solving the linear complementarity problem (LCP) arising in single and multi-asset American put option pricing. The LCP for American option is a variable coefficient parabolic model defined on an unbounded domain. Initially, using the far field estimate method and the penalty method respectively, the LCP could be reformulated into a nonlinear parabolic partial differential equation on a bounded domain. To construct a unified lattice Boltzmann model for the option pricing problems, the above transformation equations are rewritten into an equivalent divergence form. Then, through the incorporation of an amending function into the evolution equation, which assists in recovering the source term and eliminating the error term, the lattice Boltzmann model with spatial second-order accuracy is constructed. Finally, the present model is validated using numerical simulations, and the numerical results agree well with the option values obtained by existing methods, which indicates that the present lattice Boltzmann model is efficient for solving the American put option pricing problem.

The consensus tracking problem of leader-follower multi-agent systems (MASs) with singular structures on jointly connected topology is studied in this paper. To achieve the objective of consensus tracking, a distributed adaptive control protocol is formulated to adjust the coupling weights among the agents using the adaptive rate, where the adaptive protocol can be implemented by each agent in a fully distributed manner without using any global information. A fuzzy logic system method is used to deal with the nonlinear terms in response to the limitations of nonlinear system analysis. The consensus tracking problem is transformed into an error system stability analysis, and two sufficient conditions are provided to guarantee the control objective based on Lyapunov stability theory and singular system theory. Finally, the effectiveness of this method is verified through a simulation example.

In this paper, we investigate the problems of sliding mode observer design and observer-based integral sliding mode control for a class of singular bio-economic systems with stochastic disturbance. Initially, we establish a bio-economic system with the alien invasive species and stochastic disturbance. Then, a new integral sliding surface is constructed based on the multiplication of sliding variables and negative definite matrix for the error system. The advantage of this method is that it not only stabilizes the sliding variables, but also eliminates the restrictive assumptions often used in sliding mode control of the singular bio-economic systems with stochastic disturbance. Finally, an augmented system is constructed and the linear matrix inequality technique is used to determine the admissibility of the mean square exponent. Furthermore, an observer-based sliding mode controller is designed so that the reachability conditions can be guaranteed. The validity of the results is verified by a numerical simulation.

In this paper, the problem of adaptive fuzzy control for stochastic biological systems with stage structure is studied. Firstly, considering the species itself in nature will be affected by a variety of uncertain factors, a more realistic stochastic biological model is established. Then, aiming at the unknown nonlinear functions in the stochastic biological system, the fuzzy logic system (FLS) is used to approximate the unknown nonlinear terms. Secondly, the backsteppting method and adaptive fuzzy means are applied to the prey–predator model with stage structure, and the corresponding adaptive fuzzy controller is designed. It is guaranteed that all states in the biological system are semi-globally uniformly ultimately bounded (SGUUB), the juvenile prey density can track the given desired density, and the tracking error converges to a small neighborhood near zero. Finally, a simulation experiment is carried out with reference to the real case of the significant reduction of the number of lampreys. The results show that compared with the general adaptive control method, the control strategy proposed shows higher superiority in the stochastic biological system.

This paper studies the distributed optimal output agreement problem of T-S fuzzy multi-agent systems under a weight-balanced and quasi-strongly connected graph. Consider a given global convex objective function, the objective of this paper is to steer the outputs of T-S fuzzy multi-agent systems to the optimal solution of this global objective function by the partial information of the local objective functions. To achieve the objective, a novel T-S fuzzy adaptive distributed optimal algorithm is proposed to guarantee that outputs of all agents can follow the global optimal solution. Then, the stability of overall closed-loop system composed of T-S fuzzy multi-agent systems and T-S fuzzy adaptive distributed scheme is established. In order to achieve the output agreement and minimize the objective function simultaneously, a sufficient condition is obtained. Finally, a numerical example is employed to demonstrate the effectiveness and superiority of the theoretical results.