In the era of big data, the digital economy has become a key driving force for the high-quality development of tourism. Based on the annual panel data of 14 prefectures in Xinjiang from 2008 to 2018, this study proves the positive effect of the digital economy on the high-quality development of tourism. Through the construction of an evaluation index system for the high-quality development, a fixed effects model is used to investigate the relationship between them. Furthermore, mediating effect analysis is employed to study the mechanism. The robustness testing and heterogeneity analysis show the validity and rationality of the model. The results show that (1) The digital economy is an important driving force in the high-quality development of tourism in Xinjiang; (2) The digital economy promotes high-quality development by stimulating the upgrading of the tourism structure; (3) The impact of the digital economy on the high-quality development of tourism in different regions in Xinjiang presents great heterogeneity. The provincial capital presents a more significant effect.

The digital economy now plays a pivotal role in reshaping the global economic structure and optimizing the allocation of resources. With the popularization of digital technology in rural areas, the impact of the digital economy on rural development is also increasing. In order to explore the impact of the digital economy on rural revitalization in Xinjiang of China, this study constructed an indicator system based on the data from 14 prefectures or cities (of the same administrative level as the prefectures) in Xinjiang from 2013 to 2019. The entropy weight method and coupling coordination degree (CCD) model were used to analyze the digital economy level (DEL) and rural revitalization level (RRL) in Xinjiang, and the relationship between the digital economy and rural revitalization was emphasized. Finally, the obstacle degree model was used to reveal the factors that hinder the coupled and coordinated development between the digital economy and rural revitalization. The research shows that: (1) Xinjiang’s DEL generally increased steadily, and digital economy development in 14 prefectures or cities had strong spatial heterogeneity. At the same time, Xinjiang’s RRL showed similar characteristics. (2) The CCD between the two systems was increasing, and the regional distribution features of high-level CCD were in northern Xinjiang and low-level CCD in southern Xinjiang. The coupling coordination was in its infancy, but the interaction between the two systems was increasing, and the development prospect was broad. (3) Overall, the main obstacle affecting the CCD between the digital economy and rural revitalization was the digital infrastructure among four factors, including digital investment, thriving businesses, social etiquette and civility, and effective governance. The degree of this obstacle varied in different phases of coupling coordination development.

With the development of the Internet, it is more convenient for people to obtain information, which also facilitates the spread of rumors. It is imperative to study the mechanisms of rumor transmission to control the spread of rumors. The process of rumor propagation is often affected by the interaction of multiple nodes. To reflect higher-order interactions in rumor-spreading, hypergraph theories are introduced in a Hyper-ILSR (Hyper-Ignorant–Lurker–Spreader–Recover) rumor-spreading model with saturation incidence rate in this study. Firstly, the definition of hypergraph and hyperdegree is introduced to explain the construction of the model. Secondly, the existence of the threshold and equilibrium of the Hyper-ILSR model is revealed by discussing the model, which is used to judge the final state of rumor propagation. Next, the stability of equilibrium is studied by Lyapunov functions. Moreover, optimal control is put forward to suppress rumor propagation. Finally, the differences between the Hyper-ILSR model and the general ILSR model are shown in numerical simulations.

Since the issuance of the "Guiding Opinions on Vigorously Developing Sports Tourism" in 2016, the integration of sports and tourism has become a strategy in regional economic development. It creates new economic growth points, enhances local images, and promotes cultural communication. In the context of the "Tourism Makes Xinjiang Thrive" strategy, quantitatively investigating the integration of the sports and tourism industries helps people to better understand their interaction which can serve as the valuable input in policy-making for the comprehensive development of a region. This paper uses entropy weight method, stochastic frontier analysis and coupling coordination model to quantitatively analyze the effect of sports tourism industry integration in Xinjiang from the perspective of integration path. Meanwhile, the Dagum Gini coefficient and nuclear density estimation were used to analyze the regional differences and dynamic evolution of industrial integration quality. The result shows that (1) The sports and tourism integration quality in Xinjiang has not reached the optimal goal of complete integration. In the process of mutual industrial promotion, tourism promotes a higher degree of integration with the sports industry. (2) The industrial integration quality shows a phenomenon of “imbalance and inadequacy” among the regions. The regions with high quality of industrial integration were Urumqi, Ili, Kashgar, Altay and Changji, which have rich sports tourism resources. (3) The overall spatial difference in the quality of industrial integration presented a fluctuation downtrend. The difference between the tourism industrial belts was very significant.

In this paper, some tactics are considered in Xinjiang tourism industrial belt based on performance evaluation. First, we applied the Balanced Scorecard (BSC) to establish an evaluation system for Xinjiang tourism development in four dimensions: tourism performance, resource utilization, basic supporting capacity, and market attention. Second, the performance of tourism development in 14 Prefectures was evaluated using the Analytic Hierarchy Process (AHP) in 2018. Third, because the Prefectures were divided into four tourism industrial belts, a discussion was conducted to identify and understand the difference among them and their corresponding influence on regional tourism development using the Theil index and Entropy method. The result shows that (1) In all dimensions, the differences within each industrial belt were greater than those between industrial belts. (2) The tourism industrial belts displayed a differentiation phenomenon, in the dimension of significant difference being distinct for different belts. Finally (3), it is found that the resource utilization of all belts is significantly different.

In this paper, the consensus problem of high-order multi-agent systems with inherent feed-forward delayed non-linear dynamics is investigated. First, a new kind of aperiodically intermittent communication strategy, which can be regarded as an extension of continuous communication, is proposed. The time-varying delay is considered in the multi-agent systems and the delay is not restricted to less than the communication width. Moreover, in order to reach a consensus, the effect of the feed-forward non-linearity and the time-varying delay is eliminated by designing a low-gain control protocol. Based on Lyapunov stability theory, graph theory and inequality techniques, some sufficient conditions related to the input gain and the communication width are obtained for achieving the consensus. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed method.