The digital economy enhances economic efficiency and improves economic structure, driving economic growth through transformations in efficiency, momentum, and quality. It has become a new driving force for advancing common prosperity. This study uses SDM, SDID, and SPSTR models to explore the impact of digital economy on common prosperity, which constructs the index system to evaluate the common prosperity from process index and outcome index. According to the panel data of 76 cities in the Yellow River Basin from 2011 to 2021, and the findings are as follows: (1) The digital economy exhibits a development pattern characterized by high activity downstream and lower activity upstream, and the development trend is stable. The development pattern of common prosperity has changed from sporadic distribution to regional agglomeration, and the level of common prosperity in most cities has improved. (2) The digital economy has a significant positive spatial effect on common prosperity. And the findings are robust after introducing the “Big Data” exogenous policy impact, dynamic SDM model, and other methods. Moreover, spatial heterogeneity exists. The promotion effect in the upper and lower reaches is stronger, while the middle reaches are weakly affected by the digital economy. (3) The spatial spillover effect of the digital economy on common prosperity has a boundary, and the positive spillover reaches a maximum value at 600–650 km. (4) Nonlinear analysis confirms that the digital economy provides momentum for common prosperity industrial structure optimization that can effectively stimulate the “endogenous” growth mechanism, strengthen the marginal increasing effect of the digital economy driving common prosperity and enhance the effect of “making a bigger pie”. The digital economy makes effective use of digital resources and technologies, promotes the equalization of public services, exerts a positive impact on the realization of common prosperity, and consolidates the effect of “dividing a better cake”.

This paper investigates the robust stability and stabilization of networked evolutionary games (NEGs) with time delays. First, a mathematical model is presented to describe the dynamics of NEG with time-varying delays and disturbances. Second, an auxiliary system is constructed using the semi-tensor product of matrices and a dimension augmenting technique. Then, a verification condition of robust stability is derived. Third, in order to stabilize NEG to the Nash equilibrium, the robust stability problem is transformed into the robust stabilization problem. Moreover, an algorithm is proposed to design the stabilization controller. Finally, the validity of the results is verified by an example.

Grey models have attracted considerable attention as a time series forecasting tool in recent years. Nevertheless, the linear characteristics of the differential equations on which traditional grey models rely frequently result in inadequate predictive accuracy and applicability when addressing intricate nonlinear systems. This study introduces a conformable fractional order unbiased kernel-regularized nonhomogeneous grey model (CFUKRNGM) based on statistical learning theory to address these limitations. The proposed model initially uses a conformable fractional-order accumulation operator to derive distribution information from historical data. A novel regularization problem is then formulated, thereby eliminating the bias term from the kernel-regularized nonhomogeneous grey model (KRNGM). The parameter estimation of the CFUKRNGM model requires solving a linear equation with a lower order than the KRNGM model, and is automatically calibrated through the Bayesian optimization algorithm. Experimental results show that the CFUKRNGM model achieves superior prediction accuracy and greater generalization performance compared to both the KRNGM and traditional grey models.

This paper examines the impact of climate risks on urban economic resilience, using panel data from Chinese cities between 2009 and 2022. A multidimensional indicator system, encompassing recovery resilience, adaptive resilience, and transformative innovation capacity, is developed to identify how climate risks negatively affect urban economic resilience. The results show that climate risks weaken resilience by reducing population size and destabilizing financial systems. Additionally, these risks have significant spatial spillover effects, extending from local areas to neighboring cities through regional economic networks, with particular impact on geographically adjacent cities. Heterogeneity analysis indicates that developed eastern cities, central cities, and resource-based cities are more vulnerable to climate risks, while cities in central and western regions and non-central cities show greater resilience. The paper proposes policy recommendations to strengthen urban resilience, including investment in climate-adaptive infrastructure, promoting economic diversification, establishing cross-regional climate risk management, developing green finance systems, and raising public awareness of climate risks.

The integration of digital technologies has opened new space for agricultural development. Digital agriculture reshapes agricultural production relations and provides new pathways for strengthening grain supply chain resilience. Using panel data from 31 Chinese provinces (municipalities and autonomous regions) spanning 2011–2023, this paper constructs a digital agricultural technology innovation index through patent keyword matching, calculates grain supply chain resilience using a multi-dimensional indicator system, and conducts empirical analysis with two-way fixed effects, moderated mediation, and panel smooth transition regression (PSTR) models. The results show: (1) Digital agricultural technology innovation significantly increases grain supply chain resilience, with farmland transfer exerting a positive moderating effect on this relationship. (2) Digital agricultural technology innovation primarily affects grain supply chain resilience through large-scale farming operations, with agricultural insurance further reinforcing this mediation pathway. (3) The effect of digital agricultural technology innovation on grain supply chain resilience displays regional heterogeneity: the effect is negative in low-resilience regions and turns positive in high-resilience regions, and this effect exhibits nonlinear characteristics that shift from negative to positive as social consumption levels and industrial structure rationalization increase. Policy design should be stage-specific: low-resilience regions should prioritize service and capability foundations before rapid hardware expansion, medium-resilience regions should focus on cross-segment coordination, and high-resilience regions should prioritize data integration and advanced risk analytics.