This paper mainly studied the stochastic stability and the design of state feedback controllers for nonlinear singular continuous semi-Markov jump systems under false data injection attacks. Based on the Lyapunov function and the implicit function theorem, a basic stochastic stability condition of the system was given to ensure that the nonlinear singular semi-Markov jump system under attack was regular, impulse-free, unique, and stochastically stable. On this basis, the stochastic admissible linear matrix inequality conditions of the system were obtained by using the singular value decomposition of the matrix and Schur’s complement lemma. To design the state feedback controller, based on the upper and lower bounds of the time-varying transition probability of the semi-Markov jump system and the singular value decomposition method, the stochastic stable linear matrix inequality condition of the closed-loop system under the false data injection attack was established. Finally, the validity and feasibility of the results were verified by numerical examples.

The implementation of ecological pest-management strategies is an important trend in the global agricultural development, which makes integrated pest management become an important research field. In this study, to achieve a scientific and reasonable pest-management objective, three aspects of work were carried out. 1) Modeling and analysis: a pest-natural enemy Gomportz- type model with a variable searching rate was put forward, and two pest-management models were formulated. The dynamic characteristics of the continuous model were investigated, and the results indicated that the search speed of natural enemies had an effect on the coexistence equilibrium. 2) Control effect: the sliding mode dynamics of the Filippov system including the existence of pseudo- equilibrium was analyzed to illustrate the effect of the non-smooth control strategy on the system. A Poincaré map was constructed for the system with a threshold control, and the complex dynamics induced by the threshold control was investigated. 3) Verifications: computer simulations were presented step by step to illustrate and verify the correctness of the theoretical results. A comprehensive study of predation relationships as well as the effects of different management strategies on the system can serve as a valuable reference for advancing sustainable agricultural practices and pest control.

We investigate the existence of periodic solutions for nonconservative superlinear second- order differential equations in the sense of rotation numbers. Specifically, we focus on equations whose solutions at infinity behave comparably to a suitable linear system. By employing a rotation number approach, spiral analysis, and fixed-point theorems, we establish the existence of periodic solutions for nonconservative superlinear second-order differential equations. Among the equations we consider, a notable subclass is partially superlinear second-order differential equations, which provide a concrete illustration of our results. Our results extend several recent results, thereby advancing to a more comprehensive understanding of periodic behavior in nonconservative systems.

We establish an L^p_loc-existence theorem for the $\partial \bar{\partial}$-equation on a half-space of $\mathbb{C}^{n}$. The result is achieved for forms of class L^p loc as well as for those forms in the scale of W1,p loc -Sobolev spaces and admitting distributional boundary values. Some isomorphisms and regularity results in relation to de Rham, Bott–Chern, and Aeppli cohomology groups are moreover obtained.

The concept of F-manifold algebras is an algebraic expression of F-manifolds. In this paper, we provide the definition of an F-manifold color algebra, which can be viewed as a natural generalization of an F-manifold algebra. We develop the representation theory of an F-manifold color algebra and show that F-manifold color algebras admitting non-degenerate symmetric bilinear forms are coherence F-manifold color algebras. The concept of pre-F-manifold color algebras is also presented, and using this definition one can construct F-manifold color algebras. These results extend some properties of F-manifold algebras.

Discrete chaotic systems are now a meaningful research area due to their intricate dynamical characteristics. This paper introduces a novel piecewise logistic-like mapping chaotic system and rigorously establishes its Devaney chaoticity through mathematical proofs. Experimental findings demonstrate that, compared to the traditional logistic mapping, the logistic-like mapping exhibits more complex dynamic behaviors, such as bifurcation diagram, Lyapunov exponents, permutation entropy, sensitivity, and distribution of function sequences. Furthermore, in order to implement the suggested new chaotic system, a simulation circuit is designed, and a PSIM simulation model is established to validate feasibility of the simulation circuit.

This paper studied the event-triggered synchronization problem for time-delay neural networks under DoS attacks. A novel event-triggered scheme based on switching between periodic sampling and a continuous event-triggered scheme was proposed, which not only cuts down the number of data transmissions but also offsets cyberattacks. By choosing a suitable piecewise Lyapunov-Krasovskii functional and using several free-weighting matrices, sufficient conditions were established to ensure the exponential stability of the synchronization error system in the occurrence of DoS attacks. Furthermore, a co-design method was provided to acquire the desired non-fragile output-feedback control gain and event-triggering parameter. Finally, a numerical example was given to illustrate the usefulness of the proposed approach.

In this paper, we thought about the positive solutions to the semilinear parabolic equation with three exponents, and obtained several differential Harnack estimates of the positive solutions to the equation. As applications of the main theorems, we found blow-up solutions for the equation and classical Harnack inequalities. Our results generalize some recent works in this direction.

The fusion of infrared and visible images highlights the target while preserving detailed information, which helps to comprehensively capture the scene information. However, the existing methods continue to face challenges in managing the integration of global and local information, as well as enhancing the extraction of detailed image features, thus ultimately leading to constrained fusion outcomes. To enhance the fusion effect, this paper proposes a dual-branch residual attention- based infrared and visible image fusion network (TBRAFusion). The network utilizes two key modules, TransNext and the dual-branch residual attention (DBRA) module, which are used to process the input images in parallel to extract contrast and detail information. Additionally, an auxiliary function is incorporated into the loss function. Compared with mainstream fusion models, TBRAFusion achieves better fusion results and metrics through these improvements. The experimental results on the TNO dataset show that TBRAFusion improves the metrics in entropy (EN), spatial frequency (SF), sum ofcorrelation differences (SCD), and visual information fidelity (VIF) by 0.42%, 4%, 3.9%, and 1.2%, respectively. Tests on the MSRDS dataset show improvements of 1.7%, 5.4%, 9.6%, and 4.9% in EN, standard deviation (SD), SF, and SCD, respectively.

In this paper, we study geodesics of left-invariant sub-Riemannian metrics on the Cartesian square of a connected two-dimensional non-commutative Lie group, where the metric is determined by the inner product on a two-dimensional generating subspace of the corresponding Lie algebra. It is proven that the system of equations for geodesics of such a sub-Riemannian metric is not completely integrable in the class of meromorphic functions. Important qualitative characteristics of the corresponding geodesics are found, thus proving the complexity of their behavior in general.

In the realm of Unsupervised Domain Adaptation (UDA), adversarial learning has achieved significant progress. Existing adversarial UDA methods typically employ additional discriminators and feature extractors to engage in a max-min game. However, these methods often fail to effectively utilize the predicted discriminative information, thus resulting in the mode collapse of the generator. In this paper, we propose a Dynamic Balance-based Domain Adaptation (DBDA) method for self-correlated domain adaptive image classification. Instead of adding extra discriminators, we repurpose the classifier as a discriminator and introduce a dynamic balancing learning approach. This approach ensures an explicit domain alignment and category distinction, thus enabling DBDA to fully leverage the predicted discriminative information for an effective feature alignment. We conducted experiments on multiple datasets, therefore demonstrating that the proposed method maintains a robust classification performance across various scenarios.

As an emerging network architecture, software-defined networking (SDN) has the core concept of separating the control plane from the network hardware and unifying its management by a central controller. Since the centralized control of SDN is such that an attack on the controller can lead to the paralysis of the entire network, intrusion detection has become particularly significant for SDN. Currently, more and more intrusion detection systems based on machine learning and deep learning are being applied to SDN, but most have drawbacks such as complex models and low detection accuracy. This paper proposes an enhanced spider wasp optimizer (ESWO) algorithm for feature dimensionality reduction of intrusion detection datasets and constructs a new intrusion detection model (IDM), namely ESWO-IDM, for SDN. The ESWO algorithm integrates multiple strategies, including tent chaotic map strategy and elite opposition learning strategy to improve the diversity of the population, Lévy flight strategy to prevent the algorithm from falling into local optimum in the early stage, and dynamic adjustment strategy of control parameters to balance exploration and exploitation of the algorithm. ESWO was empirically evaluated using eight benchmark test functions and four UCI datasets to comprehensively demonstrate its advantages. Binary and multiclassification experiments were conducted using the InSDN dataset to analyze the ESWO-IDM performance and compare it with other IDMs. The experimental results show that the ESWO-IDM achieves the best performance in all the metrics in both binary classification and multiclassification and has the most prominent effect on the detection of normal, denial of service (DoS), distributed DoS, and Brute Force Attack types, which effectively improves SDN intrusion detection from the viewpoint of optimization.

Using the complex method, Guoqiang Dang and Qiyou Liu [Guoqiang Dang, Qiyou Liu, Electron. Res. Arch., 31 (2023), 1303–1322] have found some exact solutions of the conformable Huxley equation. In this comment, we first demonstrate that the elliptic function solutions and rational function solutions do not satisfy the complex conformable Huxley equation. Finally, all exact solutions of the conformable Huxley equation are given by us.

In this work, an energy-preserving scheme is proposed for the nonlinear Dirac equation by combining the exponential time differencing method with the scalar auxiliary variable (SAV) approach. First, the original equations can be transformed into the equivalent systems by utilizing the SAV technique. Then the exponential time integrator method is applied for discretizing the temporal derivative, and the standard central difference scheme is used for approximating the spatial derivative for the equivalent one. Finally, the reformulated systems, the semi-discrete spatial scheme, and the fully-discrete, linearly implicit exponential scheme are proven to be energy conserving. The numerical experiments confirm the theoretical results.

Using an optimal control framework, the optimization of production and maintenance processes is investigated in this paper. We focused on analyzing system behavior, managing costs, and controlling quality. Differential equations are utilized to model the relationship between inventory level, production, and maintenance strategies. A cost function is built combining different cost elements, and the optimal production and maintenance rates were obtained. A sensitivity analysis is performed to assess the impact of different parameters on the total cost and on the optimal solution. The key findings demonstrated that higher initial inventory levels significantly decreased long-term costs and improved production efficiency. The optimal preventive maintenance strategy emphasized the importance of early investments in quality and maintenance, leading to sustained operational stability.

Accurate interval prediction of wind speed plays a vital role in ensuring the efficiency and stability of wind power generation. Due to insufficient traditional wind speed interval prediction methods for mining nonlinear features, in this paper, a novel interval prediction method was proposed by combining improved wavelet threshold and deep learning (BiTCN-BiGRU) with the nutcracker optimization algorithm (NOA). First, NOA was used to optimize the wavelet transform (WT) and BiTCN-BiGRU. Second, we applied NOA-WT to smooth the wind speed data. Then, to capture nonlinear features of time series, phase space reconstruction (PSR) was utilized to identify chaotic characteristics of the processed data. Finally, the NOA-BiTCN-BiGRU model was built to perform wind speed interval prediction. Under the same hyperparameters and network structure settings, a comparison with other deep learning methods showed that the prediction interval coverage probability (PICP) and prediction interval mean width (PIMW) of NOA-WT-BiTCN-BiGRU model achieves the best balance, with good prediction accuracy and generalization performance. This research can provide reference and guidance for nonlinear time-series interval prediction in the real world.

In this paper, I define and classify the algebraic Schouten solitons associated with the Bott connection on three-dimensional Lorentzian Lie groups with three different distributions.

In this paper, we focused on the Caputo-Hadamard fractional reaction sub-diffusion equations. By using the nonuniform L1 scheme and nonuniform Alikhanov scheme in the temporal domain, we formulated two efficient numerical schemes, where the second order difference method was used in the spatial dimension. Furthermore, we derived the stability and convergence of these proposed schemes. Remarkably, both derived numerical methods exhibited α-robustness, that is, it remained valid when α → 1⁻. Numerical experiments were given to demonstrate the theoretical statements.

Energy consumption accounting and prediction in the medium and thick plate rolling process are crucial for controlling costs, improving production efficiency, optimizing equipment management, and enhancing the market competitiveness of enterprises. Starting from the perspective of integrating process mechanism and industrial big data, we overcame the difficulties brought by complex and highly nonlinear coupling of process variables, proposed a rolling power consumption accounting algorithm based on time slicing method, and gave a calculation method for the additional power consumption of the main motor for rough rolling and finishing rolling (auxiliary system power consumption, power loss, main motor power consumption deviation); with the help of SIMS model, forward recursion, and reverse recursion pass rolling force estimation strategies are proposed, and the rated power consumption of the main motor was predicted. Furthermore, a random forest regression model of additional power consumption based on data was established, and then a prediction algorithm for the comprehensive power consumption of billet rolling was given. Experiments showed the effectiveness of the proposed method.

Let $\left(u_{n}\right)_{n \geq 0}$ be the special Lucas u-sequence defined by

where n ≥ 0, B = ±1, and A is an integer such that A² − 4B > 0. Let where m, l are positive integers, s = 1, 2, 3, 4, and C is any constant. The aim of this paper is to find a form g_n such that For example, we show that

We have presented a maximum principle preserving the unconditionally stable scheme for the Allen–Cahn (AC) equation with a high-order polynomial potential. The proposed method ensures the preservation of the maximum principle, a critical characteristic for accurately modeling phase transitions and maintaining physical consistency in simulations. The proposed method uses an operator splitting technique, a numerical approach that decomposes a complex problem into simpler subproblems, solved sequentially, to improve computational efficiency and stability. The operator splitting method applied to the AC equation yields one nonlinear equation and several linear equations. To solve the nonlinear equation, we applied the frozen coefficient method, which approximates variable coefficients in differential equations by treating them as constants within small regions, simplifies the problem, and enables more efficient numerical solutions. For several linear equations, which are diffusion equations, we applied a fully implicit finite difference scheme to obtain unconditional stability. By using these methods, we achieved unconditional stability for the AC equation. To validate the superior performance of the developed algorithm, we performed computational tests. Computational experiments demonstrated its unconditional stability, particularly in handling high- order polynomial potentials. Furthermore, we highlighted a distinctive feature of the AC equation in modeling phase separation under noisy data conditions.

We study here the special decay properties of real solutions to the initial value problem associated with the (3 + 1)-dimensional modified Zakharov-Kuznetsov equation. More precisely, we prove the properties of exponential decay of order 3/2 above the plane x + y + z = 0 as time evolves. This property is related with the persistence properties of the solution flow in weighted Sobolev spaces and sharp unique continuation properties of solutions to this problem.

An improved metaheuristic algorithm called the Crossover strategy integrated Secretary Bird Optimization Algorithm (CSBOA) is proposed in this work for solving real optimization problems. This improved algorithm integrated logistic-tent chaotic mapping initialization, an improved differential mutation operator, and crossover strategies with the Secretary Bird Optimization Algorithm (SBOA) for a better quality solution and faster convergence. To evaluate the performance of CSBOA, two sets of a standard benchmark set, CEC2017 and CEC2022, were applied first. The Wilcoxon rank sum test and Friedman test were also used to statistically compare the proposed CSBOA algorithm with seven common metaheuristics. The comparisons demonstrated that CSBOA is more competitive than other metaheuristic algorithms on most benchmark functions. Additionally, the performance of CSBOA was validated for two challenging engineering design case studies. Comparative results showed that CSBOA provides more accurate solutions than the SBOA and the other seven algorithms, suggesting viability in dealing with real global optimization problems.

Considering the influence of population heterogeneity, media coverage and spatial diffusion on disease transmission, this paper investigated an acquired immunodeficiency syndrome (AIDS) reaction-diffusion model with nonlinear incidence rates and media coverage. First, we discussed the positivity and boundedness of system solutions. Then, the basic reproduction number R₀ was calculated, and the disease-free equilibrium (DFE), denoted as E⁰, was locally and globally asymptotically stable when R₀ < 1. Further, there existed a unique endemic equilibrium (EE), denoted as E^*, which was locally and globally asymptotically stable when R₀ > 1 and certain additional conditions were satisfied. In addition, we showed that the disease was uniformly persistent. Finally, the visualization results of the numerical simulations illustrated that: The media coverage was shown to mitigate the AIDS transmission burden in the population by lowering the infection peak and the time required to reach it; a higher awareness conversion rate can effectively reduce the basic reproduction number R₀ to curb the spread of AIDS.