Applied Mathematics and Computation最新文献

In game theory, the emergence and maintenance of cooperative behavior within a group is a significant topic in evolutionary game theory and complex network theory. However, the limitations of a single mechanism in traditional networks restrict a thorough analysis of the sustenance and development of cooperative behavior, given the challenges posed by the diversity of social groups. To address this issue, this paper combines reinforcement learning game strategies with traditional prisoner's dilemma strategies based on two-layer coupled network to investigate the transmission of cooperative behavior among individuals in games. In our research, we study the evolutionary pattern and phase transitions using the Monte Carlo method. We use the prisoner's dilemma game as a mathematical model, establishing two subpopulations in each layer, with mutually payoff-neutral players between different subpopulations. This configuration results in intriguing spatiotemporal dynamics and patterns, leading to the spontaneous emergence of a cyclic dominance, where defectors from one group become prey for cooperators in another group, and vice versa. By simulating game evolution, we explore individual strategy changes and the impact of individual abilities on cooperative behavior in reinforcement learning. Extensive validations indicate that, in social dilemmas, adjusting the abilities of groups through effective guidance can sustain cooperative behavior. This guidance enables us to comprehend the stability of cooperation under adverse conditions. Simultaneously, the coexistence of two subpopulations greatly amplifies the complexity of evolutionary dynamics, causing a increase in cooperation rate.

Different from the existing multiple asymptotic stability or multiple Mittag-Leffler stability, the multiple exponential stability with explicit and faster convergence rate is addressed in this paper for short memory fractional-order impulsive Cohen-Grossberg neural networks with time delay. Firstly, ${\prod }_{i=1}^n(2H_i+1)$ total equilibrium points of such n-neuron neural networks can be ensured via the known fixed point theorem. Then, by means of the theory of fractional-order differential equations, the methods of average impulsive interval and Lyapunov function, a series of sufficient conditions for determining the locally exponential stability of ${\prod }_{i=1}^n(H_i+1)$ equilibrium points are obtained based on maximum norm, 1-norm and general q-norm ($q=2^n$), respectively. This paper's research reveals the effects of impulsive function, impulsive interval, fractional order and time delay on the dynamic behaviors. Finally, four examples are proposed to demonstrate the effectiveness of theoretic achievements.

Center-based models are used to simulate the mechanical behavior of biological cells during embryonic development or cancer growth. To allow for the simulation of biological populations potentially growing from a few individual cells to many thousands or more, these models have to be numerically efficient, while being reasonably accurate on the level of individual cell trajectories. In this work, we increase the robustness, accuracy, and efficiency of the simulation of center-based models by choosing the time steps adaptively in the numerical method and comparing five different integration methods. We investigate the gain in using single rate time stepping based on local estimates of the numerical errors for the forward and backward Euler methods of first order accuracy and a Runge-Kutta method and the trapezoidal method of second order accuracy. Properties of the analytical solution such as convergence to steady state and conservation of the center of gravity are inherited by the numerical solutions. Furthermore, we propose a multirate time stepping scheme that simulates regions with high local force gradients (e.g. as they happen after cell division) with multiple smaller time steps within a larger single time step for regions with smoother forces. These methods are compared for a model system in numerical experiments. We conclude, for example, that the multirate forward Euler method performs better than the Runge-Kutta method for low accuracy requirements but for higher accuracy the latter method is preferred. Only with frequent cell divisions the method with a fixed time step is the best choice.

In this article, the problem of fixed-time active fault-tolerant control is investigated for dynamical linear systems with intermittent faults and unknown disturbances. Unlike traditional active fault-tolerant control, fixed-time control is taken into account in this article since intermittent faults appear and disappear within a certain period of time. The entire active fault-tolerant control framework is composed of fault detection, fault isolation, fault and state estimation as well as the reconfigurable controller. Using the homogeneity-based observers, states and faults are well estimated and a fault diagnosis scheme is proposed for the sake of detecting and isolating intermittent faults in a fixed time. The fault-tolerant controller, which provides global practical fixed-time stability of the closed-loop system, has two switching states corresponding to the appearance and disappearance of intermittent faults. As a consequence, intermittent faults are compensated via the designed active fault-tolerant control method and the system reaches practical stability with the entire convergence time bounded in a fixed time. Finally, two examples are exploited to demonstrate the effectiveness of theoretical results.

In this paper, a novel reinforcement learning (RL)-based adaptive event-triggered control problem is studied for non-affine multi-agent systems (MASs) with time-varying dead-zone. The purpose is to design an efficient event-triggered mechanism to achieve optimal control of MASs. Compared with the existing results, an improved smooth event-triggered mechanism is proposed, which not only overcomes the design difficulties caused by discontinuous trigger signals, but also reduces the waste of communication resources. In order to achieve optimal event-triggered control, RL algorithm of the identifier-critic-actor structure based on fuzzy logic systems (FLSs) is applied to estimate system dynamics, evaluate control performance, and execute control behavior, respectively. In addition, considering time-varying dead-zone in non-affine MASs brings obstacles to controller design, which makes system applications more generalized. Through Lyapunov theory, it is proved that the optimal control performance can be achieved and the tracking error converges to a small neighborhood of the origin. Finally, simulation proves the feasibility of the proposed method.

Recently, passivity of fractional complex networks has aroused much interest, but the concerned models contain only cooperative relationships and the competitive interaction among individuals is ignored. In this article, a class of fractional complex networks with a signed graph is considered and several conditions are derived to achieve the passivity of fractional signed networks by pinning strategies designed based on M-matrix theory. Particularly, in pinning adaptive control schemes, the pinning nodes are selected only according to the cooperative relationships among nodes and the control gains can regulate automatically to meet the actual demand. In addition, without translating the signed networks into corresponding unsigned networks based on the gauge transformation, some criteria of bipartite synchronization for fractional signed networks are obtained based on the feature of the signed topology and the derived passivity results. The theoretical results are eventually verified by several illustrate examples.

This paper investigates adaptive-estimation-based dynamic event-triggered fuzzy tracking control scheme for high-order nonlinear systems in fixed-time interval. The growing assumptions of coexistence unknown nonlinear uncertainties are removed with the aid of fuzzy logic systems. Contrary to the existing results, an adaptive estimation tactic is formulated to estimate the severe coexistence uncertainties online such that no boundaries are needed for the adaptive parameters, despite approximation errors, unknown virtual control gains and time-varying disturbances. On this estimation mechanism, the virtual control gains have been relaxed to unknown, which is more applicable. In view of controller and actuator, the communication burden is reduced with the aid of dynamic event-triggered rule, and Zeno behavior can be prevented successfully during dynamic sampling and updating of the control signal. Moreover, the singularity problem has been conquered by using the inequality transformation technique and all signals are bounded in fixed-time interval. Finally, two examples are used to verify the feasibility and rationality.

In this paper, we propose a Stable Generalized Finite Element Method (SGFEM) to address non-homogeneous elliptic interface problems with discontinuous coefficients. Our approach utilizes the homogenization method to transform non-homogeneous interface conditions into homogeneous ones, thereby facilitating the application of the SGFEM. Specifically, we construct functions that satisfy the jump conditions, streamlining the problem-solving process. In the SGFEM, enrichment functions are used to efficiently construct these specialized functions, reducing the computational demands of the homogenization method. Notably, this method involves only calculations of additional right-hand terms near the interface, which require significantly less computation compared to the calculation of the stiffness matrix, thus avoiding any alterations to the stiffness matrix and preserving the stability and robustness of the SGFEM. We apply our method in both two-dimensional and three-dimensional scenarios, employing distinct strategies for each. In the 2D examples, the displacement homogenization method simplifies the implementation by addressing only the displacement jumps, thereby reducing the computational load. In the 3D examples, the synchronous homogenization method further simplifies numerical implementation by eliminating surface integrals on the interface. Through error analysis and numerical experiments, we demonstrate the efficiency and optimal convergence of our proposed method.

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 can be introduced by breaking down the probabilities of different possible cases, and the model of strategy transition process can be constructed with the semi-tensor product (STP) of matrices. Second, through the classical ZD strategy acquisition method, the step for designing ZD strategy for multiplayer two-strategy repeated finite games under implementation errors is presented. Then, the sufficient and necessary conditions for checking the effectiveness of ZD strategy under implementation errors are studied. In addition, by distinguishing the focal player's neighbors, the current approach is extended to networked evolutionary game (NEG) under implementation errors for group decision-making, and an intelligent algorithm is also provided. Finally, we use two examples to demonstrate the validity of our proposed method.

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 of payoff equality. By assuming the similarity between the value function in “mental accounting effect” and the inverse of the Lorenz curve, the “rank strategy” is introduced in the form of a slightly alternated Fermi strategy which focuses on the rank difference on the wealth (payoff) distribution curve along the calculation of the Gini coefficient. Such introduction opens up a new perspective to the cross section between economics and the evolutionary game theory. Compared with the original Fermi strategy adoption (named payoff strategy), the rank strategy significantly aids the system to survive a higher benefit with a faster recovery after the enduring period. The reason behind this can be discussed from the formation of giant clusters, which also indicates a spillover effect in both cooperation and payoff equality improvement. A further breakdown in the population also suggests the leading role of rich players who help poor players in improving the payoff equality among them. The rank strategy is further evaluated in a broad parameter range with different combinations of the ratio of initial cooperators, the benefit (b) and the fitness (K). In most cases, the rank strategy shows a better performance in both the fraction of cooperators and the Gini coefficient, which concludes that the mental accounting effect could be the more realistic factor that may be critical to consider. The resolution in the cooperative mechanism may also be linked to wealth equality. Simulation results in this work suggest a close relationship between cooperation improvement and the payoff equality which is not extensively explored in earlier works. Simulations with Gini distribution explain “A good deed is never lost” in a numerical way.