中国科学院数学与系统科学研究院期刊网

11 May 2026, Volume 46 Issue 5
    

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  • WANG Chenbo, JI Zhijian
    Journal of Systems Science and Mathematical Sciences. 2026, 46(5): 1395-1412. https://doi.org/10.12341/jssms240557
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    In this paper, the controllability of signed multi-agent networks based on the consensus protocol is studied from the perspective of topological structure. Firstly, based on the eigenvectors of Laplacian matrix and the leader-follower structure, the necessary and sufficient algebraic condition for the controllability of undirected signed topologies is obtained. According to the condition, for the composite topologies obtained by connecting two sub-topologies, two methods are proposed to construct controllable composite topologies by connecting the controllable sub-topologies. In addition, based on uncontrollable undirected signed topologies, the same sign double controllability destructive nodes (SSDCDN) and inverse sign double controllability destructive nodes (ISDCDN) are defined for the first time. By analyzing the characteristics of these nodes, the necessary and sufficient condition for the controllability on multi-leader undirected signed topological graphs is obtained. Finally, on the basis of the existing results, the design methods of two special types of uncontrollable signed sub-topologies connected with controllable signed sub-topologies to form controllable composite signed topologies are proposed.
  • LU Zhangxin, GUAN Yongqiang, XU Shiyang
    Journal of Systems Science and Mathematical Sciences. 2026, 46(5): 1413-1430. https://doi.org/10.12341/jssms240923
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    Based on the leader-follower framework, this paper investigates the bipartite containment control problem of multi-agent systems with signed networks by using zero-sum game theory. Firstly, a two-person zero-sum game model is constructed, where two groups of leaders with conflicts of interest are regarded as two players in the game; the average distance between the final state of the follower agents and the leader agents are used as the incomes of the two players; each player chooses to connect with followers through $q$ edges at most in the game. Secondly, the properties of the game are analyzed from the perspective of interaction topology, and the results show that the number of connection edges between the two groups of leaders and followers in the optimal strategy of the game is always equal and the number is $q$. In addition, we analyze the case where each player selects only one follower agent to connect, it is concluded that when the connection edge signs of the two groups of leaders and followers are the same, the interaction topology corresponding to the circulant graph is an equilibrium topology. When the follower's interaction topology is structurally balanced graph, the payoffs of the two players are related to the number of agents in the two cells divided by the followers and the positive and negative signs of the connected edges. Finally, numerical simulation examples are given to illustrate the effectiveness of the theoretical results.
  • PENG Xiao, WANG Yijing, ZUO Zhiqiang
    Journal of Systems Science and Mathematical Sciences. 2026, 46(5): 1431-1443. https://doi.org/10.12341/jssms240711
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    In this paper, the global leader-following consensus issue of discontinuous nonlinear fractional-order multi-agent systems is addressed via hybrid control strategy. Under the framework of fractional differential inclusion, one hybrid distributed control protocol with dynamic event-triggered mechanism is proposed. By utilizing Lyapunov stability theory and algebraic graph theory, the leader-following consensus for discontinuous fractional-order multi-agent system can be achieved, and Zeno behavior is excluded. Finally, a simulation example and a simulation comparison are respectively applied to verify the correctness of the obtained results and the effectiveness of the control strategy.
  • SUN Chengyuan, WANG Xuesong, CHENG Yuhu
    Journal of Systems Science and Mathematical Sciences. 2026, 46(5): 1444-1459. https://doi.org/10.12341/jssms240662
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    The existing quality-related fault diagnosis methods fail to reveal the intrinsic relationship between faults and quality due to the increasing complexity of industrial systems, and they also do not consider system dynamics thoroughly, leading to false alarms. False alarms lead to unnecessary maintenance and affect production efficiency, which will increase equipment costs and waste human resources. This paper proposes a quality-related interval fault diagnosis method based on multilevel decomposition to address this problem. Firstly, the method takes the nonlinear relationship between quality data and process data into full consideration and constructs the data model using multilevel decomposition strategy. Secondly, high-order discrete statistics are utilized to detect the system state, and a quality-related fault detection scheme is designed. Further, the interval dynamic fault diagnosis results are given by analyzing separation trajectories of fault samples and normal ones. Finally, the effectiveness of the method in this paper is verified based on the Tennessee Eastman platform and the wind turbine system.
  • LAI Qinfei, WU Xianqing, WANG Zheyu, HE Xiongxiong
    Journal of Systems Science and Mathematical Sciences. 2026, 46(5): 1460-1473. https://doi.org/10.12341/jssms240524
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    In practice, overhead cranes usually suffer from double pendulum effects which make the control of the crane systems more complex. However, for most existing traditional control methods, people often do not take into account this double pendulum phenomenon. In addition, some trajectory planning methods have been proposed to improve work efficiency for crane systems, but the rope length in these methods is constant. To address these problems, this paper proposes a novel trajectory planning method with lifting/lowering operation for double-pendulum overhead crane. Specifically, to improve the efficiency and security of the transportation process, the trajectory is designed into three phases (acceleration, constant speed and deceleration). For each stage, the desired swing angle curve is directly constructed according to the requirements of the swing angle constraint and the zero residual swing angle, and the acceleration trajectory of the trolley is further obtained through the analysis of the dynamic equation of the double pendulum system. Then, the optimization mechanism is introduced, and the objective function about the transportation time and the maximum swing angle is constructed, and the trajectory planning problem is transformed into an optimization problem of the objective function. Finally, the simulation results are shown to verify the effectiveness of the proposed trajectory planning method.
  • FAN Jianying, WEI Yunjie
    Journal of Systems Science and Mathematical Sciences. 2026, 46(5): 1474-1492. https://doi.org/10.12341/jssms250009
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    China's policy implementation and technological evolution of the energy industry exert a substantial global influence in confronting climate challenges. Given the notable regional differences in China's economic development and resource endowments, there are significant distinctions in the distribution structures and evolutionary trajectories of energy industry technologies among various regions. This study constructs the global-China multi-region integrated assessment model, namely WITCH-China, aiming to explore the optimal evolutionary paths of energy industry technology development and carbon emissions for the selected 30 regions in China under the global temperature control scenarios. And the technological optimization evolution of energy industry is comprehensively evaluated. The findings reveal that: 1) Under policy scenarios, the consumption of coal and oil show a significant downward trend, wind and solar energy experiences a sharp increase, and the proportion of non-fossil energy consumption will exceed fossil energy for the first time in 2050. 2) Carbon emissions gradually decline with the decrease in fossil energy consumption, but due to the improvement of energy efficiency and the popularization of clean energy technology, the decline of carbon emissions gradually slows down. 3) There are obvious differences in the trend of energy consumption structure in different regions, and clean resource-rich areas, such as Qinghai, Xinjiang, Inner Mongolia, Gansu, etc., have greater development potential in clean energy, and the clean substitution potential of wind power and solar energy is the most significant. Finally, the study puts forward relevant policy suggestions for the development of China's energy industry.
  • WANG Mengru, LIU Dehai, SONG Yunting
    Journal of Systems Science and Mathematical Sciences. 2026, 46(5): 1493-1519. https://doi.org/10.12341/jssms250420
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    Rapidly allocating relief resources across multi-stage and multi-regional settings under uncertain demand is a major challenge in humanitarian logistics. This study addresses complex post-disaster scenarios characterized by incomplete demand information and dynamically changing transportation networks, and proposes a two-stage robust optimization framework that integrates artificial intelligence (AI) technology with mobile facilities (MFs) to support resource pre-positioning and multi-period relief allocation. In the first stage, mobile facilities and volunteers are pre-deployed, and AI-assisted path planning is utilized to establish an initial response configuration; in the second stage, relief supplies are allocated and delivered across multiple periods as updated demand information becomes available. The model characterizes demand uncertainty via an uncertainty set and proves, under the $L_1$-norm, its equivalence to a deterministic formulation as well as the existence of an optimal allocation strategy. Numerical experiments demonstrate that, without AI support, the robust optimization model achieves better cost performance and greater stability across different scales than deterministic and stochastic models. With the incorporation of AI, rescue costs decrease significantly for all model types, with the robust model benefiting the most, reflecting the synergistic value of combining AI and robust optimization. Sensitivity analysis further indicates that both path network complexity and individual facility capacity have substantial impacts on system performance; enhancing facility capacity can further strengthen the combined advantages of intelligent scheduling and robust optimization. This study introduces a dual-mode collaborative path-planning mechanism and a two-stage robust optimization decision-making framework, offering reliable support for resource pre-positioning, transportation scheduling, and dynamic decision-making under uncertain relief demands. The proposed framework is applicable not only to natural disasters but also to public health emergencies and supply chain disruptions. Future work may incorporate distributed robust optimization and efficient solution algorithms to enhance performance in large-scale, highly complex disaster response scenarios.
  • QU Yunchao, CHANG Junbi, WU Jianjun, LEE Der-Horng
    Journal of Systems Science and Mathematical Sciences. 2026, 46(5): 1520-1542. https://doi.org/10.12341/jssms240668
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    In recent years, the frequent occurrence of emergencies worldwide has not only severely impacted the socio-economy but also led to a large number of casualties. Emergency resource allocation is a key aspect of emergency management. When there is a shortage of supplies, transferring materials between disaster sites can improve the delivery efficiency and ensure the material needs of disaster victims. However, current research on dynamic emergency material allocation rarely considers the transfer of non-consumable materials between disaster sites, resulting in low allocation efficiency, insufficient flexibility, and lack of fairness. Therefore, this paper focuses on a scenario involving multiple supply points, multiple disaster sites, and various types of emergency materials. It establishes a dynamic allocation model that considers the transfer of materials between disaster sites, combining the allocation of materials from supply points to disaster sites and the transfer of materials between disaster sites. The model takes into account time-varying information such as supply and demand volumes, urgency of demand, transportation capacity, and road conditions, as well as the requirement that non-consumable materials must meet a certain service duration. It aims to formulate an emergency material allocation plan with efficiency and fairness as objectives, thereby improving allocation efficiency and optimizing the allocation of emergency resources. Through the solution and analysis of case scenarios, the model's effectiveness and the rationality of the allocation plan are verified in terms of emergency material scheduling efficiency, fairness, and the efficiency of considering material transfer between disaster sites.
  • SHAO Zhen, ZHU Guowei, YANG Changhui, ZHAO Wei, LI Fei, LIU Chen
    Journal of Systems Science and Mathematical Sciences. 2026, 46(5): 1543-1560. https://doi.org/10.12341/jssms240779
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    Accurately predicting and analyzing the complex trends of road transport carbon emissions among regions is crucial for setting and optimizing carbon emission reduction targets and promoting the synergy of pollution reduction and carbon reduction in the road traffic industry. Aiming at the multiple time-varying characteristics of road traffic carbon emissions, such as time-varying peaks and seasonal changes, as well as the tightly coupled spatial characteristics brought about by the interconnections of different regional transportation, this paper takes into account the differences in climate regionalization and economic geographic distribution, and constructs a multi spatio-temporal fusion interregional road traffic carbon emission prediction model, MTGCN. First of all, a time-dependent relationship between short-term fluctuations and long-term trends of carbon emissions is captured by the temporal feature extractor. On this basis, the static and dynamic adaptive map structure information is integrated, and the spatial feature extractor is used to explore the potential spatial dependence of inter-regional road traffic carbon emissions. Finally, the validity of the proposed model is verified based on the daily carbon emission data of the Yangtze River Delta region.
  • GUO Fengjia, JIA Lifen, CHEN Wei
    Journal of Systems Science and Mathematical Sciences. 2026, 46(5): 1561-1578. https://doi.org/10.12341/jssms250053
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    This paper proposes a multi-attribute reverse auction (MARA) winner determination method for fourth-party logistics integrators (4PLI) selecting third-party logistics suppliers (3PLS). The method addresses incomplete and heterogeneous information while considering 4PLI risk preferences. It employs heterogeneous decision information, including real numbers, interval numbers, and probabilistic linguistic term sets (PLTS), to describe 3PLS price and non-price attributes. A trust transmission model and a trust aggregation model are built to establish a complete social trust network. Based on this network and information similarity, a model completes incomplete bid evaluation information. Furthermore, a hyperbolic absolute risk aversion (HARA) utility function is integrated into regret theory to characterize 4PLIs' differentiated risk preferences. To handle attribute correlation, weights are determined using the Spearman correlation coefficient combined with the criteria importance through intercriteria correlation (CRITIC) method. An improved probabilistic linguistic distance measure is then defined to quantify evaluation information differences. Combining this distance measure, the attribute weighting model, and the evaluation based on distance from average solution (EDAS), an alternative selection procedure for heterogeneous decision-making information is presented. Numerical examples verify the method's effectiveness and superiority. This work extends MARA winner determination theory and provides practical methods for 4PLIs selecting partners.
  • YU Xiaohui, LIU Di, CUI Qingru
    Journal of Systems Science and Mathematical Sciences. 2026, 46(5): 1579-1598. https://doi.org/10.12341/jssms241036
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    Under the “dual-carbon” goal, advanced manufacturing enterprises take green innovation as the core of development and actively improve their competitiveness. However, the green innovation of advanced manufacturing industry is a green innovation system composed of the government, the public, and advanced manufacturing enterprises (referred to as “enterprises”). The overall green innovation efficiency of the industry should be improved through the effective synergistic development within the system. Therefore, a three-party evolutionary game model consisting of enterprises, the government and the public is developed to analyze the impacts of the government's external incentives (including incubation platforms, R&D subsidies and tax incentives) and the public's green preferences on enterprises' green innovation strategies. The study finds that: The effects of the three kinds of government external incentives to promote green innovation are not the same, among which R&D subsidies are more effective in promoting green innovation at the early stage of green innovation. When the public's green preference is increased to a certain degree, the government can no longer give any external incentives to the enterprises, and then the enterprises can realize spontaneous green innovation. In the premise of no external incentives from the government, if we want to realize the spontaneous green innovation of the enterprise, then the enterprise's Green innovation is not the higher the better. In contrast, there exists an optimal degree of green innovation, when enterprises can realize spontaneous green innovation with the lowest public green preference requirement.
  • QIAN Wuyong, GUO Kaiyi, WANG Xuan, XU Hanrong
    Journal of Systems Science and Mathematical Sciences. 2026, 46(5): 1599-1623. https://doi.org/10.12341/jssms240811
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    Vehicle routing problem in takeout delivery is characterized by dynamic order arrivals and the need for continuous updates on rider status. To address this challenge, a multi-objective dynamic optimization model maximizes the interests of customers, platforms, and riders while considering rider physical condition and road familiarity. A dynamic weights multi-objective heuristic algorithm adaptively adjusts the weights of different objectives based on real-time data, optimizing delivery paths dynamically. Results demonstrate superior performance compared to the Gurobi solver in key metrics such as order fulfillment time, rider idle time, and platform profit. This highlights the effectiveness of the method in handling the complexities of real-world takeout delivery operations. Analysis of dispatch strategies for different types of riders provides valuable insights for operational decision-making. In summary, this research offers a practical solution to enhance delivery efficiency and customer satisfaction while ensuring fair treatment of riders, contributing to improved operational strategies for takeout platforms.
  • ZHAO Lili, LIU Zhenhao, YANG Xin
    Journal of Systems Science and Mathematical Sciences. 2026, 46(5): 1624-1643. https://doi.org/10.12341/jssms240940
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    The issuance of green bonds is not only a key driver for enhancing enterprises' new quality productivity, but also an important means of deepening environmental responsibility practices. Based on the data from A-share listed enterprises from 2010 to 2022, this study employs a difference-in-differences model to analyze the impact of green bond issuance on enterprises' new quality productivity in China. The findings are as follows: 1) The issuance of green bonds significantly promotes the improvement of new quality productivity; 2) Mechanism analysis shows that the impact of green bond issuance on enterprises' new quality productivity lies in enhancing green innovation capability and reducing enterprise financing costs; 3) Heterogeneity analysis reveals that the promotion effect of green bond issuance on new quality productivity is more pronounced for non-state-owned enterprises, small and medium-sized enterprises, and high-pollution enterprises; 4) Further analysis indicates that public environmental attention and regional environmental regulations play a significant reverse moderating role in the process of improving enterprise new quality productivity. The results of this study provide empirical evidence for enhancing enterprises' new quality productivity, achieving green development transformation, and promoting high-quality development of enterprises.
  • FENG Zhongwei, REN Yuhang, TAN Chunqiao
    Journal of Systems Science and Mathematical Sciences. 2026, 46(5): 1644-1666. https://doi.org/10.12341/jssms241006
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    This paper considers a two-period dynamic system with a proprietary brand manufacturer (PCM), an original equipment manufacturer (OEM) and strategic consumers, where PCM produces end products and proprietary components (PCs), decides whether and when to provide OEM with PCs, and determines when to enter the end market. The dynamic game models are constructed to explore the effects of product quality differentiation, purchasing behavior of strategic consumers, and bargaining power on the choice of PCM's coopetition strategies. The results show that: 1) The strategy choice of PCM mainly depends on product quality differences when PCM has the independent pricing right for PCs. When OEM's product quality is low, PCM monopolizes the end market. When OEM produces high-quality products, PCM will provide OEM with PCs in the second period and enter the end market in both periods if the product quality differentiation is low, while PCM will provide OEM with PCs in the first period enter the end market in the second period if the product quality differentiation is high. 2) When PCM and OEM bargain over the wholesale price of PCs, providing components in the second period and entering the end market in both periods is PCM's inferior strategy. Whether to provide OEM with PCs in the first period and enter the end market in the second period depends on bargaining power, consumer patience, and product quality differentiation. 3) Compared to PCM's autonomous pricing situation, PCM is hurt by bargaining. However, if OEM is willing to redesign the profit-sharing mechanism, bargaining can achieve Pareto improvement in both parties' profits.
  • SHI Jilei, YIN Yilong, WEI Qi, SHAN Erfang
    Journal of Systems Science and Mathematical Sciences. 2026, 46(5): 1667-1683. https://doi.org/10.12341/jssms240960
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    In cooperative games with graph structures, the player potential function method and the inclusion-exclusion decomposability property as two important methods can be used to study the Myerson value. The probabilistic Myerson value is a kind of generalization of Myerson value in cooperative games with generalized probabilistic graph structures, this paper shall extend the player potential function method and the inclusion-exclusion decomposability property to the cooperative games with generalized probabilistic graph structures, and define the probabilistic player potential function and probabilistic inclusion-exclusion decomposability property to explore their relationship with the probabilistic Myerson value and we give new characterizations and two new calculation methods of the probabilistic Myerson value. This study finds that the probabilistic player potential function method can give a more intuitive definition of the probability Myerson value from the perspective of marginal contribution, while the probabilistic inclusion-exclusion decomposability property can better reveal the internal relationship between the probabilistic Myerson value and probabilistic graph structure, so these conclusions have good theoretical value. Finally, an example of utility sharing of enterprise cooperative coalition is given to verify the rationality of the conclusion.
  • JIAN Dan
    Journal of Systems Science and Mathematical Sciences. 2026, 46(5): 1684-1699. https://doi.org/10.12341/jssms250833
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    This paper presents a numerical method for solving a class of nonlinear complementarity problems (NCPs) motivated by traffic assignment. Building on the spectral three-term Hestenes-Stiefel (HS) conjugate gradient method (Wang, 2023) for unconstrained optimization, we extend and apply it to solve NCPs. First, we introduce a new spectral three-term HS-type search direction based on an adaptive mechanism. This direction is independent of any line search procedure and possesses sufficient descent and trust-region-like properties. By incorporating the inertial acceleration technique and an adaptive line search, we develop an inertial spectral three-term conjugate gradient projection method. Under standard assumptions, we establish the global convergence of the proposed method. Preliminary numerical experiments demonstrate that the method exhibits favorable performance compared to several existing methods for solving NCPs. Finally, the proposed method is applied to traffic assignment problems to further illustrate its practical potential.
  • FAN Jianwei, HUANG Zhenwen
    Journal of Systems Science and Mathematical Sciences. 2026, 46(5): 1700-1717. https://doi.org/10.12341/jssms250204
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    Under the dual context of profound global economic restructuring and accelerating technological revolution, this paper investigates the impact mechanisms and regional heterogeneity of new quality productive forces (NQPF) on China's foreign trade competitiveness. Utilizing provincial panel data from 2010-2021, we construct a three-tier evaluation system integrating technological, green, and digital productivity dimensions. Through fixed-effects modeling, mediation analysis, and regional heterogeneity tests, we identify two critical transmission pathways: Economic growth (dominant mediator) and industrial structure upgrading. Findings demonstrate significant regional disparities, with the eastern region exhibiting stronger NQPF effects through technology-industry synergy, contrasting with central-western regions constrained by traditional industrial path dependence and innovation resource limitations. The study validates NQPF's theoretical mechanisms in reshaping trade competitiveness through technological spillovers, factor upgrading, and industrial coordination. Policy implications emphasize differentiated regional strategies, institutional innovation, and green-digital transformation to achieve balanced NQPF development and advance China's trade competitivenes.
  • GAO Zeying, SUN Xiangkai
    Journal of Systems Science and Mathematical Sciences. 2026, 46(5): 1718-1727. https://doi.org/10.12341/jssms251057
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    This paper deals with a class of primal-dual dynamical systems with Hessian damping for solving strongly convex optimization. The existence and uniqueness theorem for the global strong solution of this system is first established. Subsequently, using Lyapunov analysis, some exponential convergence rates of the primal-dual gap, objective function residual and feasibility violation, as well as the strong convergence of the solution trajectory generated by the system are obtained. Furthermore, some numerical experiments are given to demonstrate that the system exhibits fast convergence and effectively reduces oscillation phenomena.
  • SI Linsheng, DIAO Songyuan, CUI Chunsheng, YAN Yanfei
    Journal of Systems Science and Mathematical Sciences. 2026, 46(5): 1728-1737. https://doi.org/10.12341/jssms250337
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    With the rapid development of the takeaway industry, the relay delivery model has emerged accordingly. The equitable distribution of riders' benefits is a critical factor affecting the sustainable development of this model. Based on the practical challenges of takeaway relay delivery, this study constructs a profit allocation model using Pythagorean fuzzy sets. By incorporating multidimensional indicators such as delivery distance, delivery time, and service density index, the model achieves optimized benefit distribution among riders. This research not only extends the application of Pythagorean fuzzy sets, but also provides a novel approach to addressing benefit allocation issues in takeaway relay delivery systems.
  • ZHAO Zhen, GüLISTAN Kurbanyaz, MENG Lijun, TIAN Maozai
    Journal of Systems Science and Mathematical Sciences. 2026, 46(5): 1738-1756. https://doi.org/10.12341/jssms250494
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    This paper proposes a class of spatial varying-coefficient autoregressive models with autocorrelated errors. The proposed framework simultaneously incorporates spatial correlation in the response variable and spatial autocorrelation in the error term within the spatial varying-coefficient setting, thereby jointly capturing both heterogeneity and dependency structures in spatial data to better reflect their complex characteristics. To overcome the endogeneity issue of the model, an effective three-stage estimation method is proposed that integrates local linear estimation, generalized method of moments (GMM), and profile least squares estimation methods, and the asymptotic properties of the estimators are derived. The Monte Carlo simulation results indicate that the estimation method for the studied model demonstrates good efficacy under finite samples. Empirical analysis based on the Boston housing price data further shows that this model significantly enhances the explanatory power of spatial economic phenomena.