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Early Warning Simulation of Urban Vulnerability in Coal-Resource-Based Cities Based on System Dynamics 基于系统动力学的煤炭资源型城市脆弱性预警模拟
IF 1.4 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-05-31 DOI: 10.1155/2024/8393217
Dongmei Feng, Liang Wang, Xiumei Duan
Coal-resource-based cities, as one of the important types of typical resource-based cities in China, have strong characteristics of instability, sensitivity, and fragility, exhibiting a series of vulnerability features of the human-land system. Previous studies have lacked a deeper investigation into the vulnerability of such cities from the perspective of coupling feedback mechanisms among various elements or subsystems. This paper adopts Bohle et al.’s “Dual Structure Model” of vulnerability to establish an indicator system for vulnerability warning in coal-resource-based cities. Using Fushun City as a sample, a dynamic simulation model of vulnerability in coal-resource-based cities is constructed based on system dynamics for warning simulation calculations, analyzing the evolution trend of vulnerability in Fushun City from 2010 to 2022. The results show the following: (1) from 2010 to 2022, the urban vulnerability of Fushun City transitioned from a medium warning level to a relatively safe level, showing a trend of annual reduction and improvement, undergoing three development stages of significant reduction, fluctuation stabilization, and slight rebound. (2) Due to the causal relationships among various elements within the vulnerability subsystems of Fushun City, differences exist in the contribution levels of vulnerability subsystems during the period 2010–2022, under the combined effects of sensitivity and adaptability factors. The contribution rate of the natural subsystem was the highest from 2010 to 2014, while, from 2016 to 2019, urban vulnerability began to shift towards an economically and socially dominant type. Influenced by the pandemic, Fushun City’s overall vulnerability has shown an upward trend since 2020 compared to the previous stage. Finally, specific policy suggestions are proposed for Fushun City to cope with vulnerability changes based on the analysis results, providing a theoretical basis for achieving sustainable development in such coal-resource-based cities.
煤炭资源型城市作为我国典型资源型城市的重要类型之一,具有较强的不稳定性、敏感性和脆弱性特征,表现出一系列人地系统的脆弱性特征。以往的研究缺乏从各要素或子系统间耦合反馈机制的角度对这类城市的脆弱性进行深入研究。本文采用 Bohle 等人的脆弱性 "双重结构模型",建立煤炭资源型城市脆弱性预警指标体系。以抚顺市为样本,构建了基于系统动力学的煤炭资源型城市脆弱性动态模拟模型,进行预警模拟计算,分析了抚顺市 2010 年至 2022 年的脆弱性演变趋势。结果表明(1)2010-2022年,抚顺市城市脆弱性由中度预警水平过渡到相对安全水平,呈现逐年降低和改善的趋势,经历了显著降低、波动趋稳、略有回升三个发展阶段。(2)由于抚顺市脆弱性子系统内部各要素之间的因果关系,在敏感性因子和适应性因子的共同作用下,2010-2022年期间脆弱性子系统的贡献水平存在差异。2010-2014年,自然子系统的贡献率最高,而2016-2019年,城市脆弱性开始向经济和社会主导型转变。受大流行病的影响,抚顺市总体脆弱性自2020年起较前一阶段呈上升趋势。最后,根据分析结果提出了抚顺市应对脆弱性变化的具体政策建议,为此类煤炭资源型城市实现可持续发展提供了理论依据。
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引用次数: 0
Enhancing Geopolymer Mix Optimization: Integration of the Plackett–Burman Method and Response Surface Methodology for Sustainable Construction Materials 加强土工聚合物混合优化:将普拉克特-伯曼法和响应面方法结合用于可持续建筑材料
IF 1.4 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-05-31 DOI: 10.1155/2024/6401595
N. Anuja, M. Palanivel, N. Amutha Priya
Nowadays, construction industries are using flyash as a potential alternative for cement. Due to its improved mechanical properties, ecofriendly nature, and low cost, geopolymer technology makes use of flyash as a promising future binder material. In this paper, 7 factors such as liquid-to-flyash ratio, silicate-to-hydroxide ratio, curing temperature, curing period, concentration of NaOH (molarity), rest period prior to curing, and dosage of superplasticizer that influence the compressive strength and temperature drop are screened using the Plackett–Burman method for optimization. Here, compressive strength and temperature drop are taken as the main indices of response to analyze the parameters. The significant variables determined from the Plackett–Burman design are further considered for the process of optimization using the response surface methodology. From the analysis, the optimum values of 0.4071 liquid-to-flyash ratio, 2.5 silicate-to-hydroxide ratio, and 6 hours curing period give maximum compressive strength and temperature drop of 28.87 MPa and 5.3°C under the optimized medium in the validation experiment which varies by only 3.93% and 1.85% from the observed value of 27.20 MPa and 5.4°C.
如今,建筑行业正在使用粉煤灰作为水泥的潜在替代品。由于粉煤灰具有更好的机械性能、环保性和低成本,土工聚合物技术将粉煤灰作为一种前景广阔的粘结剂材料加以利用。本文采用 Plackett-Burman 法筛选了影响抗压强度和温降的 7 个因素,如液体与粉煤灰的比例、硅酸盐与氢氧化物的比例、固化温度、固化时间、NaOH 的浓度(摩尔数)、固化前的静置时间和超塑化剂的用量,并进行了优化。其中,抗压强度和温降是分析参数的主要响应指标。从普拉克特-伯曼设计中确定的重要变量将进一步考虑使用响应面方法进行优化。分析结果表明,0.4071 液体-飞灰比、2.5 硅酸盐-氢氧化物比和 6 小时固化期的最佳值使验证实验中优化介质下的最大抗压强度和温降分别为 28.87 兆帕和 5.3 摄氏度,与观察值 27.20 兆帕和 5.4 摄氏度相比,仅相差 3.93% 和 1.85%。
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引用次数: 0
Relationship between the Significant Solutions of Static Traffic Assignment Problems for Mixed Traffic Flow of Connected and Automated Vehicles and Human-Driven Vehicles 互联和自动驾驶车辆与人类驾驶车辆混合交通流静态交通分配问题的重要解决方案之间的关系
IF 1.4 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-05-18 DOI: 10.1155/2024/9400721
Jaewoong Yun
Connected and automated vehicles can reduce the traffic congestion level of the entire network through platoon-driving technologies compared to human-driven vehicles. One promising approach to enhancing platoon-driving technology’s efficiency is deploying dedicated lanes or roads for connected and automated vehicles. Since asymmetric interactions between different vehicle types increase road congestion, it is necessary to distinguish routes for efficient traffic management. However, the traditional traffic assignment problem, which uses only user equilibrium as a constraint with no difference in travel time between users, could not be proposed as a globally optimal solution because it generates an infinite number of locally optimal solutions. Recent studies have attempted to overcome the limitations by considering the sum of system-wide travel times as an additional constraint. Their research sought to help propose optimal deployment strategies through the lowest total travel time solution (best-case) or design robust transport planning strategies through the highest total travel time solution (worst-case). However, past studies have not focused on the possibility of the best/worst case appearing in reality. This study focused on the relationship between the two solutions pointed out in past studies and traffic patterns likely to appear in reality. This study interprets the Karush–Kun–Tucker condition of the static traffic assignment problem, considering the asymmetric interaction, and proposes a solution algorithm using discrete dynamics. The proposed algorithm extends the most widely used method in transportation planning research, which can overcome the limitations of asymmetric interaction problems through simple variations. The proposed algorithm can reliably derive two solutions, and entropy theory shows that both solutions are unlikely to appear in reality without additional policies such as dedicated lanes or roads.
与人类驾驶的车辆相比,互联和自动驾驶车辆可以通过排驾技术降低整个网络的交通拥堵水平。提高排驾驶技术效率的一个可行方法是为联网和自动驾驶车辆部署专用车道或道路。由于不同类型车辆之间的非对称互动会加剧道路拥堵,因此有必要区分路线以实现高效的交通管理。然而,传统的交通分配问题只将用户均衡作为约束条件,用户之间的出行时间没有差异,因此无法提出全局最优解,因为它会产生无限多的局部最优解。最近的研究试图通过将整个系统的旅行时间总和作为额外的约束条件来克服这种局限性。他们的研究试图通过最低总旅行时间解决方案(最佳情况)来帮助提出最佳部署战略,或通过最高总旅行时间解决方案(最差情况)来设计稳健的交通规划战略。然而,以往的研究并未关注最佳/最差情况在现实中出现的可能性。本研究的重点是过去研究中指出的两种解决方案与现实中可能出现的交通模式之间的关系。本研究解释了静态交通分配问题的 Karush-Kun-Tucker 条件,考虑了非对称交互作用,并提出了一种使用离散动力学的求解算法。提出的算法扩展了交通规划研究中最广泛使用的方法,通过简单的变化克服了非对称交互问题的局限性。所提出的算法可以可靠地得出两个解决方案,而熵理论表明,如果没有专用车道或道路等附加政策,这两个解决方案在现实中都不太可能出现。
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引用次数: 0
Recycling Mode Choice in a Textile and Apparel Closed-Loop Supply Chain considering Blockchain 考虑区块链的纺织服装闭环供应链中的回收模式选择
IF 1.4 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-05-14 DOI: 10.1155/2024/6074035
Jianfeng Zhu, Tao Hang, Haodong Zheng, Xuemei Zhang
The development of the textile and apparel (T&A) industry has led to an increasing focus on recycling used products. Remanufactured product quality raises consumer concerns, and blockchain can effectively solve this problem. We establish a closed-loop supply chain (CLSC) in which a manufacturer, a retailer, or a third-party recycler collects used T&A products to examine the most efficient recycling mode with and without blockchain and the impact of blockchain on CLSC decisions. The results show that (1) if the manufacturer’s recycling cost coefficient is relatively low, used T&A products are collected directly by the manufacturer. Otherwise, the responsibility for recycling used T&A products falls to the retailer or the third-party recycler. It is noteworthy that the manufacturer’s choice of recycling mode remains unchanged whether a blockchain is implemented or not. (2) The implementation of blockchain by the manufacturer and the retailer can increase profits and consumers also benefit when the cost of validating blockchain units remains below a certain threshold. (3) When the recycling cost coefficient exceeds a certain threshold, the implementation of blockchain increases prices and recycling rates. These findings offer CLSC members’ management insights into how to select the optimal recycling mode and the consequences of implementing blockchain.
纺织品和服装(T&A)行业的发展使人们越来越关注废旧产品的回收利用。再制造产品的质量引起了消费者的担忧,而区块链可以有效解决这一问题。我们建立了一个闭环供应链(CLSC),由制造商、零售商或第三方回收商回收废旧 T&A 产品,研究有区块链和无区块链时最有效的回收模式,以及区块链对 CLSC 决策的影响。结果表明:(1)如果制造商的回收成本系数相对较低,则废旧 T&A 产品由制造商直接回收。否则,回收废旧 T&A 产品的责任就落在零售商或第三方回收商身上。值得注意的是,无论是否实施区块链,制造商对回收模式的选择都不会改变。(2)当验证区块链单位的成本低于一定阈值时,制造商和零售商实施区块链可以增加利润,消费者也会受益。(3)当回收成本系数超过一定阈值时,实施区块链会提高价格和回收率。这些研究结果为中国社区服务中心成员的管理层提供了如何选择最佳回收模式以及实施区块链的后果的启示。
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引用次数: 0
Analysis of the Dynamical Properties of Discrete Predator-Prey Systems with Fear Effects and Refuges 具有恐惧效应和避难所的离散捕食者-猎物系统的动态特性分析
IF 1.4 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-05-11 DOI: 10.1155/2024/9185585
Wei Li, Chunrui Zhang, Mi Wang
This paper examines the dynamic behavior of a particular category of discrete predator-prey system that feature both fear effect and refuge, using both analytical and numerical methods. The critical coefficients and properties of bifurcating periodic solutions for Flip and Hopf bifurcations are computed using the center manifold theorem and bifurcation theory. Additionally, numerical simulations are employed to illustrate the bifurcation phenomenon and chaos characteristics. The results demonstrate that period-doubling and Hopf bifurcations are two typical routes to generate chaos, as evidenced by the calculation of the maximum Lyapunov exponents near the critical bifurcation points. Finally, a feedback control method is suggested, utilizing feedback of system states and perturbation of feedback parameters, to efficiently manage the bifurcations and chaotic attractors of the discrete predator-prey model.
本文使用分析和数值方法研究了一类特殊的离散捕食者-猎物系统的动态行为,该系统同时具有恐惧效应和避难功能。利用中心流形定理和分岔理论计算了 Flip 和 Hopf 分岔的临界系数和分岔周期解的特性。此外,还采用数值模拟来说明分岔现象和混沌特征。结果表明,周期加倍和霍普夫分岔是产生混沌的两种典型途径,临界分岔点附近最大 Lyapunov 指数的计算也证明了这一点。最后,提出了一种利用系统状态反馈和反馈参数扰动的反馈控制方法,以有效管理离散捕食者-猎物模型的分岔和混沌吸引子。
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引用次数: 0
A Comparative Study between Time Series and Machine Learning Technique to Predict Dengue Fever in Dhaka City 预测达卡市登革热的时间序列与机器学习技术比较研究
IF 1.4 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-05-09 DOI: 10.1155/2024/2757381
Tanzina Akter, Md. Tanvirul Islam, Md. Farhad Hossain, Mohammad Safi Ullah
The dengue virus is the most dangerous one that mosquitoes may spread to people. Despite attempts by the government, dengue outbreaks are becoming increasingly common in Bangladesh. Interventions in public health rely heavily on KAP (knowledge, attitude, and practice) studies. The primary goal of this research is to forecast the occurrence of dengue disease in the city of Dhaka using methods from machine learning and time series analysis and then to compare the models in order to find the one with the lowest MAPE. From January 2016 through July 2021, monthly data were retrieved for this study from WHO and the Directorate General of Health and Services (DGHS). According to the findings of this research, neural networks outperform time series analysis when it comes to making predictions. The best-fitted neural network (NN) model was found in model 04 with 05 hidden layers which produced the minimum error model with the value of error 0.003032557, and the values of RMSE and MAPE are 7.588889e − 06 and 1.15273, respectively, for the prediction of the dengue fever in Dhaka city. In contrast, the original dengue data in the time series analysis is not stationary. Take the difference and run the unit root test by the augmented Dickey–Fuller (ADF) test to make it stationary. The dengue data series is stationary at the first-order difference, as evidenced by the ACF and PACF, which show no noticeable spike in the first-order difference. The ARIMA (6, 1, 1) model with the lowest AIC = −251.8, RMSE = 0.0310797, and MAPE = 15.2892 is the best choice model for predicting the dengue death rate. Therefore, from these two models, the NN model gives better prediction performance with the lowest value of MAPE. So, the neural network gives better prediction performance than time series analysis. The NN model forecasted 12-month death rates of dengue fever that suggest the death rate in dengue fever falling month by month. This study is more innovative than any other research because this research approach is different from any other research approach. The model selection criteria are based on the most effective performance metrics MAPE, indicating the lowest error and better prediction performance. Therefore, from this research, the author suggests machine learning gives better prediction performance than time series analysis for any other prediction performance.
登革热病毒是蚊子可能传播给人类的最危险的病毒。尽管政府做出了种种努力,但登革热疫情在孟加拉国还是越来越常见。公共卫生干预主要依靠 KAP(知识、态度和实践)研究。本研究的主要目标是利用机器学习和时间序列分析方法预测达卡市登革热病的发生率,然后对模型进行比较,以找出 MAPE 最低的模型。本研究从 2016 年 1 月至 2021 年 7 月从世界卫生组织和卫生与服务总局(DGHS)获取了月度数据。研究结果表明,神经网络在预测方面优于时间序列分析。在对达卡市登革热的预测中,具有 05 个隐藏层的模型 04 是拟合效果最好的神经网络(NN)模型,该模型产生的误差最小,误差值为 0.003032557,RMSE 和 MAPE 值分别为 7.588889e - 06 和 1.15273。相比之下,时间序列分析中的登革热原始数据并不是静态的。取其差值,通过增强 Dickey-Fuller 检验(ADF)进行单位根检验,使其成为静态。从 ACF 和 PACF 可以看出,登革热数据序列在一阶差分处是静止的,一阶差分处没有明显的尖峰。AIC=-251.8、RMSE=0.0310797、MAPE=15.2892 最低的 ARIMA(6,1,1)模型是预测登革热死亡率的最佳选择模型。因此,在这两个模型中,神经网络模型的预测性能更好,MAPE 值最低。因此,神经网络比时间序列分析具有更好的预测性能。神经网络模型预测了 12 个月的登革热死亡率,表明登革热死亡率逐月下降。本研究与其他研究相比更具创新性,因为本研究方法与其他研究方法不同。模型选择标准基于最有效的性能指标 MAPE,表明误差最小,预测性能更好。因此,通过这项研究,作者认为机器学习比时间序列分析具有更好的预测性能。
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引用次数: 0
Limit Cycles and Local Bifurcation of Critical Periods in a Class of Switching Equivariant Quartic System 一类开关等式四元系中临界期的极限循环和局部分岔
IF 1.4 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-05-02 DOI: 10.1155/2024/4786384
Jian Yang, Jukun Liu, Jingping Lu
In this paper, the limit cycles and local bifurcation of critical periods for a class of switching equivariant quartic system with two symmetric singularities are investigated. First, through the computation of Lyapunov constants, the conditions of the two singularities to become the centers are determined. Then, we prove that there are at most 18 limit cycles with a distribution pattern of 9-9 around the two symmetric singular points of the system. Numerical simulation is conducted to validate the obtained results. Furthermore, by calculating the period constants, we determine the conditions for the critical point to be a weak center of finite order. Finally, the number of local critical periods that bifurcate from the equilibrium point under the center conditions is discussed. This study presents the first example of a quartic switching smooth system with 18 limit cycles and 4 local critical periods bifurcating from two symmetric singular points.
本文研究了一类具有两个对称奇点的开关等变四元系的极限循环和临界期的局部分岔。首先,通过计算 Lyapunov 常数,确定了两个奇点成为中心的条件。然后,证明在系统的两个对称奇点周围最多存在 18 个极限循环,其分布规律为 9-9。我们进行了数值模拟来验证所获得的结果。此外,通过计算周期常数,我们确定了临界点成为有限阶弱中心的条件。最后,讨论了在中心条件下从平衡点分叉的局部临界期的数量。本研究首次提出了一个具有 18 个极限周期和 4 个局部临界期的四元切换平滑系统从两个对称奇异点分叉的例子。
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引用次数: 0
Global Flow of Foreign Aid and Change in Recipients’ Local Labor Institutions 外国援助的全球流动与受援国当地劳工机构的变化
IF 1.4 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-04-09 DOI: 10.1155/2024/1147752
Shuzhen Niu, Xiang Gao, Zhenhua Gu, Yingchao Zhang, Qian Wei
How does foreign aid affect recipient countries’ labor institutions? Extant empirical evidence is sparse due to ambiguous theoretical predictions and potential endogeneity issues. This study uses data detailing aid flow and institutional functions to mitigate such inconclusiveness and displays originality by constructing a concise theoretical framework in which foreign aid contributes to the improvement of the labor institutions in recipient countries through two mechanisms—economic growth purpose and expected aid attraction. The findings indicate that only aid to enhance local economic growth provides incentives to change domestic labor markets. Such effects have a more crucial influence on labor institutions of minimum wage, collective bargaining rights, and working hours than those related to hiring and firing regulations, mandated costs for worker dismissal, and conscription. For comparison with the actual aid level, we construct forecasted proxies to capture exogenous fluctuations in aid, determining that domestic labor markets can also change via a novel mechanism, as the recipient voluntarily mimics the funder’s labor policies in anticipation of receiving future aid, with exact amounts derived from the noninstitutional characteristics of pairs of bilateral recipient and giver economies. Therefore, we provide policy implications for the aid giver on how to secure a continued and increased aid flow and for the aid receivers on which aspects of reforming measures are most effective in enhancing the labor market regulations.
外国援助如何影响受援国的劳动体制?由于理论预测不明确和潜在的内生性问题,现有的经验证据并不丰富。本研究利用援助流量和制度功能的详细数据来缓解这种不确定性,并通过构建一个简明的理论框架来显示其独创性,在这个框架中,外国援助通过两种机制--经济增长目的和预期援助吸引力--促进受援国劳动制度的改善。研究结果表明,只有以促进当地经济增长为目的的援助才会激励国内劳动力市场发生变化。这种效应对最低工资、集体谈判权和工作时间等劳动制度的影响比那些与雇佣和解雇规定、解雇工人的法定成本和征兵相关的影响更为关键。为了与实际援助水平进行比较,我们构建了预测代用指标来捕捉援助的外生波动,从而确定国内劳动力市场也会通过一种新的机制发生变化,即受援国在预期获得未来援助的情况下自愿模仿资助国的劳动力政策,而具体数额则来自于双边受援国和援助国的非制度特征。因此,我们为援助方提供了如何确保持续和增加援助流量的政策启示,也为受援方提供了哪些方面的改革措施能最有效地加强劳动力市场监管的政策启示。
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引用次数: 0
Bézier Cubics and Neural Network Agreement along a Moderate Geomagnetic Storm 贝塞尔立方体与神经网络在中度地磁暴中的一致性
IF 1.4 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-03-26 DOI: 10.1155/2024/3559969
Emre Eroglu, Mehmet Emir Koksal
The discussion models the IRI-2012 TEC map over a moderate geomagnetic storm period (5 days) in February 2015 and compares the yield of the models. The models are constructed with the help of cubic Bézier curves and machine learning. In a sense, the comparison of a classical and mechanical approach with a modern and computer-based one is a considerable experience for the paper. The parametric curve approach governs models of piecewise continuous Bézier cubics, while the models employ only the TEC map. The design is separated into curve components at every five-hour curvature point, and each component is handled independently. Instead of the traditional least squares method for finding control points of cubics, it utilizes the mean of every five-hour of the piecewise curves of the TEC data. Accordingly, the prediction error can be controlled at a rate that can compete with the modern network approach. In the network model, 120 hours of the solar wind parameters and the TEC map of the storm are processed. The reliability of the network model is assessed by the (R) correlation coefficient and mean square error. In modeling the TEC map with the classical approach, the mean absolute error is 0.0901% and the correlation coefficient (R) score is 99.9%. The R score of the network model is 99.6%, and the mean square error is 0.71958 (TECU) (at epoch 47). The results agree with the literature.
讨论对 2015 年 2 月中度地磁暴期间(5 天)的 IRI-2012 TEC 图进行建模,并比较模型的收益。这些模型是在立方贝塞尔曲线和机器学习的帮助下构建的。从某种意义上说,将经典的机械方法与现代的计算机方法进行比较是本文的一个重要经验。参数曲线方法适用于片断连续贝塞尔立方体模型,而模型仅采用 TEC 地图。设计在每五个小时的曲率点上分成若干曲线组件,每个组件独立处理。它没有采用传统的最小二乘法来寻找立方体的控制点,而是利用了 TEC 数据中每五小时分段曲线的平均值。因此,预测误差的控制率可与现代网络方法相媲美。在网络模型中,要处理 120 小时的太阳风参数和风暴的 TEC 图。网络模型的可靠性通过(R)相关系数和均方误差来评估。在用经典方法对 TEC 地图建模时,平均绝对误差为 0.0901%,相关系数 (R) 得分为 99.9%。网络模型的 R 得分为 99.6%,均方误差为 0.71958 (TECU)(第 47 个历元)。结果与文献一致。
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引用次数: 0
Dynamic Analysis of a Simple Cournot Duopoly Model Based on a Computed Cost 基于计算成本的简单库诺二元垄断模型的动态分析
IF 1.4 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-03-25 DOI: 10.1155/2024/9912671
S. S. Askar, Ahmad M. Alshamrani
The paper is organized to study some mathematical properties and dynamics of a simple Cournot duopoly game based on a computed quadratic cost. The time evolution of this game is described by a two-dimensional noninvertible discrete time map using the bounded rationality mechanism. For this map, some dynamic characteristics such as multistability and synchronization are investigated. Its equilibrium points are obtained for the asymmetric case, and their conditions of stability are obtained. Our results investigate that the Nash equilibrium point may be unstable due to flip bifurcation and under certain parameter values, and Neimark–Sacker bifurcation is born after the period-4 cycle. Through some restrictions, the coordinate axes of the map construct an invariant manifold, and therefore, their dynamics can be analyzed by using a one-dimensional map. In the symmetric case, both firms behave identically, and this implies that the diagonal set forms an invariant manifold, and hence the synchronization phenomena take place. Furthermore, the global bifurcation of the map is confirmed through contact between critical curves and the boundaries of infeasible domains.
本文旨在研究基于二次成本计算的简单库诺二元垄断博弈的一些数学性质和动态。该博弈的时间演化由一个使用有界理性机制的二维非可逆离散时间映射来描述。研究了该图的一些动态特征,如多稳和同步。得到了非对称情况下的均衡点及其稳定性条件。我们的结果表明,纳什均衡点可能因翻转分岔而不稳定,并且在某些参数值下,Neimark-Sacker 分岔出现在周期-4 之后。通过一些限制条件,映射的坐标轴构造了一个不变流形,因此可以用一维映射来分析它们的动态。在对称情况下,两家公司的行为完全相同,这意味着对角集构成了一个不变流形,从而出现了同步现象。此外,通过临界曲线与不可行域边界之间的接触,也证实了该图的全局分岔。
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引用次数: 0
期刊
Discrete Dynamics in Nature and Society
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