In this paper, we investigate a duopolistic market with heterogeneous firms under the assumptions of an isoelastic demand and quadratic costs. We obtain the sufficient and necessary condition of the local stability of the Cournot–Nash equilibrium and analytically compare it with that of the analogue model under linear rather than quadratic costs. By approaches of symbolic computation, we prove that diseconomies of scale have an effect of stabilizing the game provided that the cost parameters are large enough. Moreover, by means of numerical simulations, we find that our model loses its stability only through a period-doubling bifurcation, which is different from its analogue having two possible routes to chaotic dynamics.

Background: Galangin, a flavonoid compound, is derived from Alpinia officinarum Hance. Previous studies have shown that galangin can inhibit the proliferation of hepatocellular carcinoma (HCC), but its mechanism is still unclear. This study aims to investigate the potential targets and molecular mechanisms of galangin on HCC through network pharmacology, bioinformatics, molecular docking, and experimental in vitro validation. Methods: In this study, network pharmacology was used to investigate the targets and mechanisms of galangin in the treatment of HCC. AutoDockTools software was used to simulate and calculate the binding of galangin to its core targets. GO and KEGG enrichment analyses were conducted in the DAVID database to explore the main biological functions and signaling pathways impacted by galangin intervention. In addition, bioinformatics was applied to examine the correlation between the differential expressions of the anti-HCC core targets of galangin and the survival of patients with HCC. Finally, the findings obtained from network pharmacology and bioinformatics were verified in cell experiments. Results: A total of 67 overlapping target genes of galangin and HCC were identified. Through the analysis of the protein-protein interaction (PPI) network, 10 hub genes with the highest degree of freedom were identified, including SRC, ESR1, MMP9, CDK4, CCNB1, MMP2, CDK2, CDK1, CHK1, and PLK1. These genes were found to be closely related to the degradation of the extracellular matrix, signal transduction, and the cell cycle. GO and KEGG enrichment analyses revealed that galangin exerts an anti-HCC role by affecting various signaling pathways, including the cell cycle, pathways in cancer, and the PI3K-Akt signaling pathway. The results of molecular docking indicated a significant interaction between galangin and CCNB1, CDK4, CDK1, and PLK1. Bioinformatics analysis revealed that CCNB1, CDK4, CDK1, and PLK1 were upregulated in the liver of patients with HCC at both the mRNA and protein levels. Flow cytometry analysis showed that galangin induced G0/G1 phase arrest and cell apoptosis in HepG2 and Huh7 cells. Additionally, galangin suppressed the expression of key proteins and mRNAs involved in the cell cycle pathway. Conclusions: These results suggest that galangin inhibits the growth of HCC cells by arresting the cell cycle at the G0/G1 phase.

Purpose: To elucidate the potential mechanisms of QFY for the treatment of Alzheimer’s Disease (AD), and explore the effective substances of QFY. Materials and Methods: UPLC-LTQ-Orbitrap-MS was used to identify the chemical constituents of the serum samples and the cerebrospinal fluid samples of rats after QFY administration. Network pharmacology was used to predict potential targets and pathways of QFY against AD. The AD mice model was established by subcutaneous injection of D-gal for 8 consecutive weeks. New object recognition (NOR) and Morris water maze test (MWM) were used to evaluate the learning and memory abilities of mice. Moreover, the levels of TNF-α, IL-1β, and IL-18 in the brain hippocampus of mice were determined by ELISA. The expression of Bax, Bcl-2, Caspase-1, PSD95, SYP, ICAM-1 and MCP-1 proteins in the hippocampus was detected by Western blotting. Furthermore, qRT-PCR was used to detect the gene expressions of PSD95, SYP, M1 and M2 polarization markers of microglia, including iNOS, CD16, ARG-1, and IL-10 in the hippocampus. Results: A total of 51 prototype compounds were detected in rat serum and 15 prototype components were identified in rat cerebrospinal fluid. Behavioral experiments revealed that QFY significantly increased the recognition index, decreased the escape latency, increased the platform crossing times and increased the residence time in the target quadrant. QFY also could alleviate the ultrastructural pathological changes in the hippocampus of AD mice. Meanwhile, QFY treatment suppressed the expression of inflammatory factors, such as TNF-α, IL-1β, and IL-18. QFY improved the synaptic plasticity of the hippocampus in D-gal model mice by significantly increasing the expression of proteins and mRNAs of PSD95 and SYP. Conclusion: QFY could effectively improve the learning and memory impairment of D-gal-induced AD mice by inhibiting the excessive activation of microglia, enhancing the expression of M2 microglia, inhibiting the increase of inflammatory factors, cell adhesion factors and chemokines, anti-apoptosis, and improving synaptic plasticity. Graphical Abstract:

In this paper, we introduce a Cournot duopoly game that can characterize fierce competition in digital economies and employ it to examine the effects of research and development (R&D) spillovers while considering various competition intensities. We obtain the analytical solution of the Nash equilibrium and the expression of commodity price, firm production, and variable profit under some key competition intensities. Furthermore, we analyze the local stability of the Nash equilibrium and derive that the equilibrium may lose its stability only through a 1:4 resonance bifurcation. Numerical simulations are conducted, through which we find that the Nash equilibrium transitions to complex dynamics through a cascade of period-doubling bifurcations. Phase portraits are also provided to illustrate more details of the dynamics, which confirm the previous theoretical finding that the Nash equilibrium loses its stability through a 1:4 resonance bifurcation.