经济系统的有效和稳定运行是实现繁荣社会和可持续世界发展的关键。然而，该系统面临不可避免的极端事件扰动，并经常受到损害。为了保持系统的稳定性，恢复受损功能至关重要。经济系统的靶向救助策略是指通过仅修复受损的经济部门来恢复系统功能的策略。这是一种重要的策略，可以减轻不可避免的极端事件造成的社会经济损失，同时能够作为增强系统的韧性并提供极端事件的早期警告之外的补充措施。这种策略比旨在恢复整体网络功能的策略更为有效。

具体来说，本研究提出了一种基于网络理论和经济均衡理论的靶向救助方法，用于抵御经济系统受到局部攻击的扰动。这是一种新颖的方法，它识别了一组与受冲击经济部门有相互强化作用的经济部门，因此被直观地被称为靶向强化路径（TRP）方法。我们开发了一个非线性动态模型，模拟经济系统在受到局部攻击后的动态运行过程，并基于靶向救助方法对受到冲击后的经济系统进行恢复，通过计算该过程的驰豫时间来量化方法的效率。此外，我们采用排名聚合方法，通过研究三个国家级经济系统（中国、印度和日本）在73种不同区域攻击情景下的靶向恢复过程来全面衡量方法的效率。为了证明方法的有效性和适用性，我们介绍了四类共六个靶向救助方法和指标来进行对比分析，这些指标分别是（1）本研究提出的靶向强化路径方法的TRP.G和TRP.T指数；（2）经典多区域投入产出方法，记作IO；（3）反向传播路径方法，记作RP-Katz；（4）根据经济部门总产出和总需求大小确定的直接救助方法，分别记作X和F。

通过研究我们发现以下结论：

从总体上看，TRP.G无论在中国、印度还是日本都具有最高的靶向恢复效率（它在中国、印度、日本对应的驰豫时间分别为18.6、9.1和13.5年）。其作为整个极端冲击情境下表现最好的方法的次数也最多，45/37。于此同时，TRP.T，X和IO有相似的表现，但是表现稍弱于TRP.G。TRP.T和X作为整个极端冲击情境下表现最好的方法的次数均为12/73，IO作为整个极端冲击情境下表现最好的方法的次数为4/73。相比之下，RP-Katz方法无论在中国、印度还是日本的靶向恢复效率都最低（它在中国、印度、日本对应的驰豫时间分别为23.7、15.8和17年）。它和F作为整个极端冲击情境下表现最好的方法的次数为0。这一结果证明，从整体上看，本文提出的靶向强化路径方法比其他方法要好，而RP-Katz方法表现较差。体现出在应对经济系统靶向救助这一问题时，需要综合利用经济系统的相关信息，仅从结构分析出发是不够的。

（2）从细节上看，对于中国的经济系统，当关键经济部门数量超过40的时候，TRP.G指标表现的最好，而TRP.T和IO表现的相近且仅次于TRP.G。此外，F在关键经济部门数量低于40时表现的最好，此时，IO和X有相近的表现但是都仅次于F。对于印度的经济系统，当关键经济部门数量超过45且小于70的时候，TRP.G方法表现的最好，而TRP.T和IO方法有相近的表现却仅次于TRP.G方法。在关键经济部门数量处于其他情况下，IO的表现是最好的。对于日本的经济系统，当关键经济部门数量超过30的时候，TRP.T方法表现的最好，而TRP.G和IO具有相似的表现但是仅次于TRP.T方法。于此同时，若关键经济部门数量小于30，IO方法表现的最好。根据上述结果可以发现，各种靶向救助方法表现的好坏会受到刺激的关键经济部门的数量的影响。对于本研究提出的TRP方法，当关键经济部门数量较少时，其表现不突出，但是当关键经济部门数量较多时，其表现较好。相对比之下，IO方法在关键经济部门数量较少时能表现的比较好，这还因为它的目标是找到最能提升待救助经济部门总产的部门，其计算不会受到靶向强化路径的影响。

（3）通过进一步研究发现，这一结果说明靶向强化路径方法的表现与经济系统的关联紧密度之间呈负向关系这是因为如果系统关联紧密度较强，靶向强化回路会广泛存在于系统中，无论IO方法还是TRP方法都会涉及很多靶向强化回路，使其救助效果表现相近。而在关联不太紧密的经济系统，本研究算法的优越性才更能凸显出来。此外，我们还发现，若以IO方法作为标杆，TRP方法的驰豫时间无论在中国、印度还是日本的经济系统中均比IO方法短0.2年。考虑到本研究中驰豫时间与经济成本直接相关，0.2年对应中国20亿元，对应印度200亿卢比，对应日本2000亿日元。总的来说，本研究提出的方法在靶向恢复效率、经济成本等多个方面均有较好的表现，说明其能够应对极端冲击后经济系统的救助问题，而靶向救助策略作为一种新的方法，具有较好的应用场景，值得进一步的深化研究。

本文的创新点是：

（1）从经济带动效应分析的视角展开研究。本课题关注到恢复力和抵抗力是一对非对称的逆问题，从系统增长角度挖掘具有经济带动效应的产业突破了传统研究从系统破坏角度出发的思路。不仅在方法上进行了创新，更从研究视角上对有关经济稳定性问题的研究进行了重要补充。

（2）针对靶向节点的经济救助展开研究。基于极端冲击往往造成局部性影响的现实，本课题重点关注靶向节点的救助问题。研究中强调挖掘靶向节点的局部异质特征，突破了传统研究更多依靠全局信息进行分析的思路。在理论上，能够提升关键节点识别算法的精准度；在实践上，能够提高相关政策效率和质量。

（3）从动态非线性过程中信息反馈的视角切入研究。本课题强调“信息反馈中涵盖节点拓扑属性和其他非线性交互特征信息”的算法设计思想，突破了传统研究依靠拓扑信息的思路。基于这一思想建模不仅能够挖掘靶向节点信息，更为后续实现经济恢复中的动态自适应优化等更加深入的研究奠定了基础。

The effective and stable operation of the economic system is crucial for achieving a prosperous society and sustainable global development. However, this system faces inevitable disruptions from extreme events and is often damaged. It is essential to restore the functionality of the system in order to maintain its stability and recover from the damages incurred. Targeted recovery strategies for the economic system refer to the approach of restoring the functionality of the system by repairing only the damaged economic sectors. This is an important strategy that can alleviate socioeconomic losses caused by inevitable extreme events and serve as a supplement to enhance the resilience of the system and provide additional measures beyond early warning of extreme events. This strategy is more effective than strategies aimed at restoring the overall network functionality.

Specifically, this study proposes a targeted recovery method based on network theory and economic equilibrium theory to counter disturbances to the economic system caused by local attacks. This novel method identifies a group of economic sectors that have mutually reinforcing interactions with the driven economic sectors and is intuitively referred to as the Targeted Reinforcement Path (TRP) method. We developed a nonlinear dynamic model to simulate the dynamic operation of the economic system after a local attack and used the targeted recovery method to restore the impacted economic system. The efficiency of the method was quantified by calculating the relaxation time of the process. In addition, we used a ranking aggregation method to comprehensively measure the efficiency of the method by studying the targeted recovery process in 73 different regional attack scenarios of three national-level economic systems (China, India, and Japan). To demonstrate the effectiveness and applicability of the method, we introduced four categories of six targeted assistance methods and indicators for comparative analysis: (1) TRP.G and TRP.T indices proposed in this study; (2) the classical multi-regional input-output method, referred to as IO; (3) the reverse propagation path method, referred to as RP-Katz; and (4) the direct recovery method based on the total output and total demand of economic sectors, referred to as X and F, respectively.

Based on our research, the following conclusions were drawn:

(1) Overall, TRP.G exhibits the highest targeted recovery efficiency in China, India, and Japan (with relaxation times of 18.6, 9.1, and 13.5 years, respectively). It also performs the best among all methods in the entire extreme shock scenarios, with the highest number of instances (45/37). TRP.T, X, and IO show similar performances but slightly weaker than TRP.G. TRP.T and X are the best-performing methods in 12/73 extreme shock scenarios, while IO is the best-performing method in 4/73 scenarios. In contrast, RP-Katz exhibits the lowest targeted recovery efficiency in China, India, and Japan (with relaxation times of 23.7, 15.8, and 17 years, respectively) and has zero instances of being the best-performing method. These results indicate that, overall, the proposed TRP method outperforms other methods, while RP-Katz performs poorly. It demonstrates the need to comprehensively utilize relevant information of the economic system when addressing targeted assistance issues rather than relying solely on structural analysis.

(2) In detail, for China's economic system, TRP.G performs the best when the number of critical economic sectors exceeds 40, followed closely by TRP.T and IO. Additionally, F performs the best when the number of critical economic sectors is below 40, with IO and X showing similar performances but slightly weaker than F. For India's economic system, TRP.G performs the best when the number of critical economic sectors exceeds 45 but is below 70, followed closely by TRP.T and IO. In other cases, IO performs the best. For Japan's economic system, TRP.T performs the best when the number of critical economic sectors exceeds 30, with TRP.G and IO showing similar performances but slightly weaker than TRP.T. Meanwhile, IO performs the best when the number of critical economic sectors is below 30. Based on these results, it can be observed that the performance of various targeted assistance methods is influenced by the number of critical economic sectors targeted. For the TRP method proposed in this study, its performance is not outstanding when the number of critical economic sectors is small but improves as the number increases. In contrast, the IO method performs relatively well when the number of critical economic sectors is small because its objective is to identify the sectors that can most effectively increase the total output of the assisted sectors, without considering the impact of targeted reinforcement paths.

(3) Further research revealed that these results indicate a negative relationship between the performance of the TRP method and the density of interconnections within the economic system. If the system exhibits strong interconnections, targeted reinforcement paths will be widespread within the system, and both the IO and TRP methods will involve many targeted reinforcement paths, resulting in similar assistance effects. In less densely interconnected economic systems, the superiority of the algorithm proposed in this study becomes more prominent. Furthermore, we found that the relaxation time of the TRP method is 0.2 years shorter than that of the IO method when benchmarked against IO. Considering that the relaxation time in this study is directly related to economic costs, 0.2 years corresponds to CNY 2 billion in China, INR 20 billion in India, and JPY 200 billion in Japan. Overall, the proposed method exhibits good performance in terms of targeted recovery efficiency, economic costs, and other aspects, demonstrating its ability to address the issue of economic system assistance after extreme shocks. The targeted assistance strategy, as a new approach, has favorable application prospects and deserves further in-depth research.

The innovations of this study are as follows:

(1) It explores the research on economic stability from the perspective of economic driving effects. This project focuses on the inverse problem of resilience and resistance, and by exploring industries with economic driving effects from the perspective of system growth, it breaks through the traditional approach of studying from the perspective of system destruction. It not only introduces innovation in methods but also provides important supplements to the research on economic stability issues from a research perspective.

(2) It focuses on the economic recovery of targeted nodes. Based on the reality that extreme shocks often cause localized impacts, this project focuses on the recovery of targeted nodes. The research emphasizes the exploration of the local heterogeneous characteristics of targeted nodes, breaking through the traditional approach of relying more on global information for analysis. In theory, it can improve the accuracy of critical node identification algorithms, while in practice, it can improve the efficiency and quality of related policies.

(3) It approaches the research from the perspective of information feedback in dynamic nonlinear processes. This project emphasizes the algorithm design concept of "information feedback encompassing node topological attributes and other nonlinear interaction characteristics," breaking through the traditional approach of relying solely on topological information. Modeling based on this concept not only allows for the exploration of targeted node information but also lays the foundation for further research, such as dynamic adaptive optimization in economic recovery.