The zero-determinant (ZD) strategy provides a new perspective for describing the interaction between players, and the errors among them will be an important role in designing ZD strategy, which attracts a lot of researches in various fields. This paper investigates how to design ZD strategy for multiplayer two-strategy repeated finite game under implementation errors. First, the implementation errors

The secret behind cooperation with the present profit-pursuing nature has been unveiled via the Evolutionary Game Theory and models. However, the payoff equality is not sufficiently explored. This paper proposes a simple but efficient way to focus on the synergetic behaviors of payoff equality and cooperation improvement. Herein, the classical Evolutional Game model is re-evaluated from the perspective

The goal of this work is to propose a new type of constraint for linear programs: inequalities having infinite, finite, and infinitesimal values in the right-hand side. Because of the nature of such constraints, the feasible region polyhedron becomes more complex, since its vertices can be represented by non-purely finite coordinates, and so is the optimum of the problem. The introduction of such constraints

In real life, a good reputation generally brings positive returns to individuals. For example, merchants with numerous good reviews usually gain higher profits. Considering this in the ultimatum game, we propose a reputation-based reward mechanism to investigate the evolution of fairness. Specifically, individuals' reputations evolve dynamically based on the outcomes of games. At the same time, we

The harmonic numbers and higher-order harmonic numbers appear frequently in several areas which are related to combinatorial identities, many expressions involving special functions in analytic number theory, and analysis of algorithms. The aim of this paper is to study the degenerate harmonic and degenerate higher-order harmonic numbers, which are respectively degenerate versions of the harmonic and

This paper introduces a novel temporal second-order fully discrete approach of finite element method (FEM) and its fast two-grid FEM on non-uniform meshes, which aims to solve non-linear time-fractional variable coefficient mobile/immobile (MIM) equations with a solution exhibiting weak regularity. The proposed method utilizes the averaged L1 formula on graded meshes in the temporal domain to handle

The Functional Quantization (FQ) method was developed for the approximation of random processes with optimally constructed finite sets of deterministic functions (quanta) and associated probability masses. The quanta and the corresponding probability masses are collectively called a “”. A method called “Functional Quantization by Infinite-Dimensional Centroidal Voronoi Tessellation” (FQ-IDCVT) was

In this paper, we propose nonlinear conjugate gradient methods for vector optimization on Riemannian manifolds. The concepts of Wolfe and Zoutendjik conditions are extended to Riemannian manifolds. Specifically, the existence of intervals of step sizes that satisfy the Wolfe conditions is established. The convergence analysis covers the vector extensions of the Fletcher–Reeves, conjugate descent, and

Basic algebraic and combinatorial properties of finite vector spaces in which individual vectors are allowed to have multiplicities larger than 1 are derived. An application in coding theory is illustrated by showing that multispace codes that are introduced here may be used in random linear network coding scenarios, and that they generalize standard subspace codes (defined in the set of all subspaces

In this paper, we introduce novel analytical solutions for valuating volatility derivatives, including volatility options and capped/floored volatility swaps, employing discrete sampling within the framework of the Merton jump-diffusion model, which is driven by a nonhomogeneous Poisson process. The absence of a comprehensive understanding of the probability distribution characterizing the realized

This paper studies the adaptive distributed unknown input observer (ADUIO) for linear systems with local outputs, which contains a group of local observers under directed graph. The difficulty is the adaptive estimation of global output for the systems with unknown inputs. To solve the problem, disturbance decoupling principle and leader-following consensus strategy are integrated to estimate local

The parallel row ordering problem (PROP) is concerned with arranging two groups of facilities along two parallel lines with the goal of minimizing the sum of the flow cost-weighted distances between the pairs of facilities. As the main result of this paper, we show that the insertion neighborhood for the PROP can be explored in optimal time by providing an -time procedure for performing this task,

This paper studies the stability problem of switched systems with state-dependent delayed impulses (SDDIs), where switching times satisfy the definition of average dwell-time. Firstly, the pulse phenomenon of the systems with SDDIs is avoided under some necessary assumptions. Subsequently, the state-dependent delayed impulsive switched systems can be transformed into the corresponding time-dependent

This paper achieves the synchronization of delayed neural networks (DNNs) considering aperiodic sampled-data control and communication delay. First of all, based on the master-slave DNNs with aperiodic sampling synchronization controller, a synchronization error system is constructed. Then, an augmented functional containing both the error state and its derivative is constructed. Compared with the

Luo et al. conjectured that for a tree with bipartition and , if a -connected bipartite graph with minimum degree at least , then has a subtree isomorphic to such that is -connected. Although this conjecture has been validated for spiders and caterpillars in cases where , and also for paths with odd order, its general applicability has remained an open question. In this paper, we establish the validity

Globally, there is a widespread awareness of poverty-related challenges. It's important to acknowledge that poverty is one of the key factors influencing prostitution. Addressing the rise in prostitution due to economic challenges is a major concern among the general public. In that scenario, many poor family girls/women were ready to downgrade their status for their family welfare and necessary needs

This article investigates the stabilization property for the modeled memristive bidirectional associative memory neural networks with time-varying delay when the faulty signals received from the fluctuated controller. The non-fragile output-feedback controller is taken into account to counteract the impact of gain perturbations to end up with robust fault-tolerant setup. To tackle the weak signals

This study addresses the problem of attack-compensated asynchronous output feedback control for stochastic switching systems with sojourn probability. Unlike traditional Markov/semi-Markov models that rely on transition probabilities, a novel switching rule is introduced that focuses on sojourn probability information associated with the target mode and sojourn time, which are easier to obtain than

Let be a graph and let denote the number of Laplacian eigenvalues of in the interval . For a tree T with diameter , Guo, Xue, and Liu proved that . In this paper, we provide a lower bound for when is a unicyclic graph, in terms of the diameter and girth of . Moreover, for the lollipop graph, under certain conditions on its diameter and girth, we give a formula for the exact value of .

We study optimal investment and insurance demand in a continuous-time model that combines risky assets with an insurable background risk. This risk takes the form of a jump-diffusion process that reduces the return rate of the agent's wealth. The main distinctive feature of our model is that the agent's decision on portfolio choice and insurance demand causes nonlinear friction in the dynamics of the

We derive stability estimates for three commonly used radial basis function (RBF) methods to solve hyperbolic time-dependent PDEs: the RBF generated finite difference (RBF-FD) method, the RBF partition of unity method (RBF-PUM) and Kansa's (global) RBF method. We give the estimates in the discrete -norm intrinsic to each of the three methods. The results show that Kansa's method and RBF-PUM can be

The manner epidemics occurs in a social network depends on various elements, with two of the most influential being the relationships among individuals in the population and the mechanism of transmission. In this paper, we assume that the social network has a homogeneous random topology of Erdös-Rényi type. Regarding the contagion process, we assume that the probability of infection is proportional

Characterizing the graph having the maximum or minimum spectral radius in a given class of graphs is a classical problem in spectral extremal graph theory, originally proposed by Brualdi and Solheid. Given a graph , a vertex subset is called a maximum generalized 4-independent set of if the induced subgraph dose not contain a 4-tree as its subgraph, and the subset has maximum cardinality. The cardinality

In this article, we present an error estimation in the norm referring to three wave models with variable coefficients, supplemented with initial and boundary conditions. The first two models are nonlinear wave equations with Dirichlet, Acoustics, and nonlinear dissipative impenetrability boundary conditions, while the third model is a linear wave equation with Dirichlet, Acoustics, and linear dissipative

Given with for , let denote the non-uniform complete hypergraph on vertices, whose edge set contains copies of every -subset of vertex set for . Let denote for for . Recently, He et al. determined all such that has a 1-factorization. In this manuscript, we consider the 1-factorization of and obtain the following results. (1) If for and , then has a 1-factorization for sufficiently large . (2) If has

This paper deals with the Turing bifurcation and pattern dynamics of a Lotka-Volterra model with the predator-taxis and the homogeneous no-flux boundary conditions. To investigate the pattern dynamics, we first give the occurrence conditions of the Turing bifurcation. It is found that there is no Turing bifurcation when predator-taxis disappears, while the Turing bifurcation occurs as predator-taxis

This paper considers the problem of trajectory tracking and collision avoidance for a class of high-order nonlinear strict feedback systems with unknown nonlinearities. The main issue is how to ensure collision avoidance and tracking performance simultaneously in the presence of unknown nonlinear functions. To address the issue, an integral-multiplicative barrier Lyapunov function (BLF) is integrated

Blind image deblurring (BID) is a procedure for reducing blur and noise in a deteriorated image. In this process, the estimation of the original image, as well as the blurring kernel of the degraded image, is done without or with only partial information about the imaging system and degradation. This is an inverse problem (ill-posed) that corresponds to the direct problem of deblurring. To overcome

This paper focuses on the problem of dynamic event-triggered predefined-time adaptive attitude control of quadrotor unmanned aerial vehicle (QUAV) suffering from unknown deception attacks. The command filter is utilized to avoid the “explosion of complexity” problem, while concurrently eliminating the effect of filtered error by constructing the fractional power error compensation signals. By using

In this paper, a dynamic event-driven optimal control scheme is proposed for the zero-sum differential graphical games in nonlinear multiagent systems with full-state constraints. Initially, to address the dual demands of optimality and state constraints, a set of system transformation functions are introduced to satisfy the state constraints of the agents. Then, by applying the principle of differential

In this paper, a new computational topological framework for hypergraph analysis and recognition is developed. “Topology provides scale” is the principle at the core of this set of algebraic topological tools, whose fundamental notion is that of a scale-space topological model (-model). The scale of this parameterized sequence of algebraic hypergraphs, all having the same Euler-Poincaré characteristic

A signed graph Σ is a graph whose edges yield the signs ±1. Let be the complete graph with vertices and be a signed complete graph, where is a subgraph induced by the negative edges of Σ. The least Laplacian eigenvalue of Σ is the least eigenvalue of its Laplacian matrix. A unicyclic graph is a connected graph containing exactly one cycle. In this paper, we focus on the least Laplacian eigenvalue of

In this paper we introduce an efficient numerical method in order to solve Volterra integral equations (VIE) of the second type. We are motivated by the fact that the coupled PDE-ODE model, used to describe the metastatic tumor growth, can be reformulated in terms of VIE, whose unknowns are biological observables, such as the cumulative number of metastases and the total metastatic mass. Here in particular

This paper introduces three local structure-preserving algorithms for the one-dimensional nonlinear Schrödinger equation with power law nonlinearity, comprising two local energy-conserving algorithms and one local momentum-conserving algorithm. Additionally, we extend these local conservation algorithms to achieve global conservation under periodic boundary conditions. Theoretical analyses confirm

We discuss a new high accuracy compact exponential scheme of order four in space and two in time to solve the three-dimensional quasi-linear parabolic partial differential equations. The derived half-step discretization based scheme is implicit in nature and demands only two levels for computation. The generalization of the proposed exponential scheme for the system of the quasi-linear parabolic PDEs

Our study investigates the dynamics of disease interaction and persistence within populations, exploring various epidemic scenarios, including backward bifurcation and cross-immunity effects. We establish conditions under which the disease-free equilibrium of the model demonstrates local or global asymptotic stability, contingent on the efficacy of quarantine measures. Notably, we find that a strain

This study is concerned with reachable set bounding of delayed second-order memristive neural networks (SMNNs) with bounded input disturbances. By applying an analytic method, some inequality techniques and an adaptive control strategy, a sufficient condition of reachable set estimation criterion is derived to guarantee that the states of delayed SMNNs are bounded by a compact ellipsoid. A non-reduced

In this paper, we investigate and implement a numerical method that is based on the mimetic finite difference operator in order to solve the nonlinear Allen–Cahn equation with periodic and non-periodic boundary conditions. In addition, we also analyze the performance of this mimetic-based method by using the classical heat equation with a variety of boundary conditions. We assess the performance of

In the present paper, uniform hyperbolic polynomial (UHP) B-spline based collocation method is proposed for solving advection-diffusion equation (ADE) numerically. The Von-Neumann's criterion is used to perform stability analysis. It reveals that the proposed scheme is unconditionally stable. The proposed method is implemented on various examples and numerical outcomes which are reported in table.

Corruption of third-party judges seriously undermines the level of cooperation. Without intervention, more corruptors and defectors would emerge, disrupting social harmony. Therefore, introducing an anti-corruption mechanism is crucial for the evolution of cooperation. In this paper, we propose a social monitoring mechanism to monitor third-party judges so that their payoffs are affected by the proportions

This research introduces an extended application of neural networks for solving nonlinear partial differential equations (PDEs). A neural network, combined with a pseudo-arclength continuation, is proposed to construct bifurcation diagrams from parameterized nonlinear PDEs. Additionally, a neural network approach is also presented for solving eigenvalue problems to analyze solution linear stability

In this paper, we construct a nonlinear evolutionary game model to analyze the cooperation mechanisms of the population based on a nonlinear relationship among environment and strategies. In the model, replicator dynamics and aspiration dynamics are used to explore the evolutionary outcomes of collective decision, respectively. The results suggest that the environment tends to become progressively

In López, Pagola and Perez (2009) we introduced a modification of the Laplace's method for deriving asymptotic expansions of Laplace integrals which simplifies the computations, giving explicit formulas for the coefficients of the expansion. On the other hand, motivated by the approximation of special functions with two asymptotic parameters, Nemes has generalized Laplace's method by considering Laplace

A graph is called -extendable if for any matching of size in , there exists a perfect matching of containing . Let and be the degree diagonal matrix and the adjacency matrix of , respectively. For , the spectral radius of is called the -spectral radius of . In this paper, we give a sufficient condition for a graph to be -extendable in terms of the -spectral radius of and characterize the corresponding

In the past few years, tensor robust principal component analysis (TRPCA) which is based on tensor singular value decomposition (t-SVD) has got a lot of attention in recovering low-rank tensor corrupted by sparse noise. However, most TRPCA methods only consider the global structure of the image, ignoring the local details and sharp edge information of the image, resulting in the unsatisfactory restoration

The paper addresses the issue of the finite-time energy-to-peak quantized filtering for Takagi-Sugeno (T-S) fuzzy systems under event-triggered-based weighted try-once-discard (WTOD) protocol, considering deception attacks in the network. To process the measurement output and schedule the transmission sequence for relieving the communication burden, a dynamic quantizer and an event-triggered-based

In the context of an edge-coloured graph , a path within the graph is deemed when a colour is exclusively applied to one of its edges. The presence of a conflict-free path connecting any two unique vertices of an edge-coloured graph is what defines it as . The , indicated by , is the fewest number of colours necessary to make conflict-free connected. Consider the subgraph of a connected graph , which

One of the crucial problems in combinatorics and graph theory is characterizing extremal structures with respect to graph invariants from the family of chemical trees. Cruz et al. (2020) presented a unified approach to identify extremal chemical trees for degree-based graph invariants in terms of graph order. The exponential augmented Zagreb index () is a well-established graph invariant formulated

The interaction between strategy and environment widely exists in nature and society. Traditionally, evolutionary dynamics in finite populations are described by the Moran process, where the environment is constant. Therefore, we model the Moran process with environmental feedbacks. Our results show that the selection intensity, which is closely related to the population size, exerts varying influences

Binarization for degraded text images has always been a very challenging issue due to the variety and complexity of degradations. In this paper, we first construct a thresholding function for the input image in a local manner and then present an anisotropic diffusion equation with a source involving dynamic thresholding function. This dynamic thresholding function is governed by an auxiliary evolution

The transmission of a vertex in a connected graph is the sum of distances from that vertex to all other vertices. A graph is transmission-irregular (TI) if no two of its vertices have the same transmission. Xu et al. (2023) recently asked to establish methods for constructing new TI graphs from the existing ones and also about the existence of chemical TI graphs on every even order. We show that, under

Delay differential equations have been used to model numerous phenomena in nature. We extend the previous work of one of the authors to analyze the stability properties of the explicit exponential Rosenbrock methods for stiff differential equations with constant delay. We first derive sufficient conditions so that the exponential Rosenbrock methods satisfy the desired stability property. We accomplish

In terms of fishery management, if it is not managed carefully, it will lead to the extinction of the species and other unfavorable conditions. In order to strengthen the protection, development and rational utilization of fishery resources, this paper proposes a population capture model with state feedback control based on previous studies, in which the small fish is influenced by the Allee effect

Traditionally, the evolution of cooperation on structured population assumed the uniform interaction partner between gaming and learning. Yet in real-world society, individuals often act different roles in which environments gaming partners differ from learning partners. This investigation studies the evolution of cooperation under the effects of the diverse selection intensity induced by network asymmetry

There have been numerous studies on collective behavior, among which communication between agents can have a great impact on both the payoff and the cost of making decisions. Research usually focuses on how to improve the collective synchronization rate or accelerate the process of cooperation under given communication cost constraints. In this context, evolutionary game theory (EGT) and reinforcement

Research on reputation-based indirect reciprocity has found profound achievements, elucidating its role in promoting cooperation over selfish actions. However, some evaluation methodologies have limitations, such as the image scoring model, a classic first-order paradigm. Several studies have suggested that higher-order rules with more individual information can enhance the stability of cooperation

Cellular Automata (CA) is a qualitative simulation method widely used in complex systems. However, the anisotropy of the bottom grid is influenced by the sharp boundary, which leads to the problem of grid-induced anisotropy. It not only makes the CA show the anisotropy in the simulation of isotropic propagation, but also produces errors in the simulation of anisotropic propagation. Through a simple

For a graph , the general atom-bond sum-connectivity index is formulated by , where indicates the degree of vertex , can be arbitrary real number. Several physicochemical features of benzenoid hydrocarbons can be correctly anticipated using the index. Researchers go through careful inspection of some and reveal that , , , enjoy benefit in foreseeing the boiling point, the standard enthalpy of vaporization

A new approach to overcome the ill-conditioning of the Method of Fundamental Solutions (MFS) combining Singular Value Decomposition (SVD) and an adequate change of basis was introduced in as MFS-SVD. The original formulation considered polar coordinates and harmonic polynomials as basis functions and is restricted to the Laplace equation in 2D. In this work, we start by adapting the approach to the

The physical interpretation of a variable-order fractional diffusion equation within the framework of the multiple trapping model is presented. This interpretation enables the development of a numerical Monte Carlo algorithm to solve the associated subdiffusion equation. An important feature of the model is variation in energy density of localized states, when the detailed balance condition between