This study investigates the dynamical properties and cycle length bifurcations of the following fifth‐order nonlinear difference equation: , where the system parameters are non‐negative, denoted as a , b , c ∈ [0, ∞ ), and the initial values are strictly positive, defined as t i ∈ (0, ∞ ) for i = −4, −3, −2, −1, 0. Utilizing the semicycle analysis technique, we establish that the lengths of successive positive and negative semicycles for any nontrivial solution demonstrate periodic regularities, specifically yielding prime periods of 30 and 2. The precise sequential patterns within a single period manifest as either 2 − , 5 + , 1 − , 1 + , 2 − , 1 + , 3 − , 2 + , 5 − , 1 + , 1 − , 2 + , 1 − , 3 + or an alternating 1 − , 1 + , 1 − , 1 + configuration. Furthermore, the present work rigorously demonstrates the global asymptotic stability of the equation’s positive equilibrium point. To corroborate our analytical findings, numerical simulations consisting of three distinct examples are provided.
Digital transformation (DT) is reshaping China’s economic structure and development model, and whether it can effectively promote China’s high-level opening-up is worthy of in-depth study. Therefore, using the provincial panel data of China from 2013 to 2023, this study examines the impact of DT on the coordinated and balanced growth of two-way FDI in China. The results show that: (1) DT can significantly promote the coordinated growth of two-way FDI (CGTFDI), and this conclusion is supported by a series of robustness tests and endogenous treatment. (2) Healthcare service efficiency can play an active mediating role in the influence of DT on CGTFDI. (3) With the increase of the level of CGTFDI, the promotion effect of DT on it will be enhanced. (4) In areas with higher environmental regulation intensity, stronger scientific and technical innovation ability and lower dependence on foreign investment, DT has a stronger promotion effect on CGTFDI. (5) DT can have a positive spatial spillover effect on CGTFDI, thus enabling regional two-way FDI to achieve coordinated and balanced growth. The conclusion of the study is instructive for realizing high-level opening-up in the digital age.
The linear Diophantine fuzzy set (LDFS) is a generalization of the complex LDFS (CLDFS), developed as a mathematical framework for optimization, soft computing, and decision-making. This paper integrates graph theory with CLDFS by introducing complex linear Diophantine fuzzy graphs (CLDFGs), which generalize several existing concepts, including Pythagorean fuzzy graphs (PFGs), intuitionistic fuzzy graphs (IFGs), and linear Diophantine fuzzy graphs (LDFGs). In this work, we extend key properties of classical graph theory to CLDFGs, focusing on operations such as composition, join, union, and the Cartesian product. Each of these operations is demonstrated with examples, and significant results are obtained for the composition, Cartesian product, and join of two CLDFGs. Moreover, we explore homomorphisms in CLDFGs, and equivalence relations via isomorphisms between CLDFGs are defined. In addition, important results regarding the complement of a CLDFG are presented. Finally, we demonstrate an application of CLDFGs in predicting earthquake risks and intensities. Overall, this research strengthens the theoretical foundation of fuzzy graph theory and offers innovative approaches to complex decision-making, thereby advancing the field of CLDFSs.
With the rapid development of the platform economy, the food delivery industry has evolved into a multisided interactive ecosystem centered on platforms, merchants, and delivery riders. Initially, the Chinese food delivery market was dominated by competition between Meituan and Ele.me; however, with JD.com’s entry, a three-way battle for market share has emerged. This study constructs a tripartite game model of online-to-offline (O2O) food delivery under duopoly and triopoly structures. In this model, the platform first sets strategic variables such as service quality levels, merchants then formulate pricing strategies based on these variables, and riders choose service effort levels based on the incentives and order volume. Starting from key variables such as commission rate, fulfillment incentive intensity, and service quality, the model characterizes the mechanism of mutual influence among the parties’ strategies under platform dominance. Based on this mechanism, simulation models are used to plot the impact of key parameters (e.g., fulfillment cost θ and incentive intensity λ) on total three-party profits, and a comparative analysis is conducted on the overall profit performance of the food delivery supply chain under duopoly and triopoly structures. Results indicate the following: (1) Increasing incentives or reducing fulfillment costs can increase the total profit of all three parties. (2) In highly competitive environments, higher platform commission rates struggle to offset the negative effects of rising fulfillment costs and may exacerbate profit erosion. (3) Marginal platforms, such as JD Takeout, which has just entered the market, are more vulnerable to shocks in fulfillment costs. (4) Service quality improvements across different platforms affect market share differently. This study extends platform game theory to oligopolistic scenarios, providing theoretical support and practical guidance for platform companies in designing incentive mechanisms and commission policies amid intense competition.
Respiratory diseases and the severity associated with infections by human respiratory viruses contribute significantly to global morbidity, mortality, and economic burden. In particular, superspreader individuals pose a significant public health challenge in the transmission of respiratory viruses. This study focuses on the formulation, analysis, and simulation of a deterministic SI1I2HCR compartmental model to explore the effect of superspreaders on the dynamics of respiratory disease. The qualitative analysis begins with the determination of DFE and EE, as well as stability, and proceeds to investigate the bifurcation and sensitivity analysis of the model. The simulation was performed using the Runge–Kutta method of order four–five. The results of the study show that reducing the transmission rate of superinfectious individuals and increasing the hospitalization rate of infected individuals as well as recovery rates significantly reduce disease spread. In addition, increasing population immunity and the treatment administered to patients in the ICU and hospitalized individuals also control the spread of the disease. We recommend that policymakers and government stakeholders prioritize immunization and treatment programs, increase public awareness, and enhance early detection through genome sequencing and data-driven surveillance to identify superspreaders and reduce the burden of disease outbreaks.
