Hopf Bifurcation Analysis in a Modified Price Differential Equation Model with Two Delays

The paper investigates the behavior of price differential equation model based on economic theory with two delays. The primary aim of this thesis is to provide a research method to explore the undeveloped areas of the price model with two delays. Firstly, we modify the traditional price model by considering demand function as a downward opening quadratic function, and supply and demand functions both depending on the price of the past and the present. Then the price model with two delays is established. Secondly, by considering the price model with one delay, we get the stable interval. Regarding another delay as a parameter, we studied the linear stability and local Hopf bifurcation. In addition, we pay attention to the direction and stability of the bifurcating periodic solutions which are derived by using the normal form theory and center manifold method. Afterwards, the study turns to simulate the results through numerical analysis, which shows that the provided method is valid

Hopf Bifurcation Analysis for the Modified Rayleigh Price Model with Time Delay

This paper mainly modifies and further develops the Reyleigh price model. By modifying the basic Reyleigh model, we can more accurately illustrate the economic phenomena with price varying. First, we research the dynamics of the modified Reyleigh model with time delay. By employing the normal form theory and center manifold theory, we obtain some testable results on these issues. The conclusion confirms that a Hopf bifurcation occurs due to the existence of stability switches when the delay varies. Finally, some numerical simulations are given to illustrate the effectiveness of our results

Stability analysis of different control modes of grid-connected converters under different grid conditions

With the sustained popularity of renewable energy generation, high penetration of variable energies, e.g., wind and solar, is reshaping the form of power systems and weakening the strength of the grid. The stability mechanism of the grid-connected converter in a weak power network, however, has yet to be evaluated. This paper establishes impedance and transient models for Grid-Following (GFL) as well as Grid-Forming (GFM) converters through the impedance analysis method and equal area criterion analysis method. The stability of these two control methods is then comprehensively studied under small and large interference with different grid conditions. The analytical results show that the GFM control is more stable against small disturbances in a weak network. In contrast, it is prone to a significant disturbance stability problem in the strong grid due to the large grid impedance. The GFL control is more suitable for a vigorous power grid, whereas introducing oscillation in a weak power grid due to its negative damping. Simulation experiments have verified the accuracy of the analytical results

The Protective Effects of Ciji-Hua’ai-Baosheng II Formula on Chemotherapy-Treated H22 Hepatocellular Carcinoma Mouse Model by Promoting Tumor Apoptosis

Ciji-Hua’ai-Baosheng II Formula (CHB-II-F) is a traditional Chinese medical formula that has been shown in clinical practice to relieve side effects of chemotherapy and improve quality of life for cancer patients. In order to understand the mechanism of its protective effects on chemotherapy, mice with transplanted H22 hepatocellular carcinoma were employed in this study. Ninety-two mice were injected subcutaneously with H22 HCC cell suspension into the right anterior armpit. After mice were treated with 5-fluorine pyrimidine (5-FU), they were divided into six groups as untreated group, 5-FU group, 5-FU plus Yangzheng Xiaoji Capsule group and three groups of 5-FU plus different concentrations of CHB-II-F. Twenty mice were euthanized after 7 days of treatment in untreated and medium concentration of CHB-II-F groups and all other mice were euthanized after 14 days of treatment. Herbal components/metabolites were analyzed by UPLC-MS. Tumors were evaluated by weight and volume, morphology of light and electron microscope, and cell cycle. Apoptosis were examined by apoptotic proteins expression by western blot. Four major components/metabolites were identified from serum of mice treated with CHB-II-F and they are β-Sitosterol, Salvianolic acid, isobavachalcone, and bakuchiol. Treatment of CHB-II-F significantly increased body weights of mice and decreased tumor volume compared to untreated group. Moreover, CHB-II-F treatment increased tumor cells in G0-G1 transition instead of in S phase. Furthermore, CHB-II-F treatment increased the expression of pro-apoptotic proteins and decreased the expression anti-apoptotic protein. Therefore, CHB-II-F could improve mice general condition and reduce tumor cell malignancy. Moreover, CHB-II-F regulates apoptosis of tumor cells, which could contribute its protective effect on chemotherapy

Crosstalk of RNA methylation writers defines tumor microenvironment and alisertib resistance in breast cancer

BackgroundThe five major RNA methylation modifications (m6A, m1A, m6Am, m5C, and m7G) exert biological roles in tumorigenicity and immune response, mediated mainly by “writer” enzymes. Here, the prognostic values of the “writer” enzymes and the TCP1 role in drug resistance in breast cancer (BC) were explored for further therapeutic strategies.MethodsWe comprehensively characterized clinical, molecular, and genetic features of subtypes by consensus clustering. RNA methylation modification “Writers” and related genes_risk (RMW_risk) model for BC was constructed via a machine learning approach. Moreover, we performed a systematical analysis for characteristics of the tumor microenvironment (TME), alisertib sensitivity, and immunotherapy response. A series of experiments in vitro were carried out to assess the association of TCP1 with drug resistance.ResultsOne “writer” (RBM15B) and two related genes (TCP1 and ANKRD36) were identified for prognostic model construction, validated by GSE1456, GSE7390, and GSE20685 cohorts and our follow-up data. Based on the patterns of the genes related to prognosis, patients were classified into RMW_risk-high and RMW_risk-low subtypes. Lower RMW_Score was associated with better overall survival and the infiltration of immune cells such as memory B cells. Further analysis revealed that RMW_Score presented potential values in predicting drug sensitivity and response for chemo- and immunotherapy. In addition, TCP1 was confirmed to promote BC alisertib-resistant cell proliferation and migration in vitro.ConclusionRMW_Score could function as a robust biomarker for predicting BC patient survival and therapeutic benefits. This research revealed a potential TCP1 role regarding alisertib resistance in BC, providing new sights into more effective therapeutic plans

Dynamic Methylation Changes of DNA and H3K4 by RG108 Improve Epigenetic Reprogramming of Somatic Cell Nuclear Transfer Embryos in Pigs

Background/Aims: DNA methylation and histone modifications are essential epigenetic marks that can significantly affect the mammalian somatic cell nuclear transfer (SCNT) embryo development. However, the mechanisms by which the DNA methylation affects the epigenetic reprogramming have not been fully elucidated. Methods: In our study, we used quantitative polymerase chain reaction (qPCR), Western blotting, immunofluorescence staining (IF) and sodium bisulfite genomic sequencing to examine the effects of RG108, a DNA methyltransferase inhibitor (DNMTi), on the dynamic pattern of DNA methylation and histone modifications in porcine SCNT embryos and investigate the mechanism by which the epigenome status of donor cells’ affects SCNT embryos development and the crosstalk between epigenetic signals. Results: Our results showed that active DNA demethylation was enhanced by the significantly improving expression levels of TET1, TET2, TET3 and 5hmC, and passive DNA demethylation was promoted by the remarkably inhibitory expression levels of DNMT1, DNMT3A and 5mC in embryos constructed from the fetal fibroblasts (FFs) treated with RG108 (RG-SCNT embryos) compared to the levels in embryos from control FFs (FF-SCNT embryos). The signal intensity of histone H3 lysine 4 trimethylation (H3K4me3) and histone H3 lysine 9 acetylation (H3K9Ac) was significantly increased and the expression levels of H3K4 methyltransferases were more than 2-fold higher expression in RG-SCNT embryos. RG-SCNT embryos had significantly higher cleavage and blastocyst rates (69.3±1.4%, and 24.72±2.3%, respectively) than FF-SCNT embryos (60.1±2.4% and 18.38±1.9%, respectively). Conclusion: Dynamic changes in DNA methylation caused by RG108 result in dynamic alterations in the patterns of H3K4me3, H3K9Ac and histone H3 lysine 9 trimethylation (H3K9me3), which leads to the activation of embryonic genome and epigenetic modification enzymes associated with H3K4 methylation, and contributes to reconstructing normal epigenetic modifications and improving the developmental efficiency of porcine SCNT embryos

Hopf Bifurcation Analysis for the Model of the Chemostat with One Species of Organism

We research the dynamics of the chemostat model with time delay. The conclusion confirms that a Hopf bifurcation occurs due to the existence of stability switches when the delay varies. By using the normal form theory and center manifold method, we derive the explicit formulas determining the stability and direction of bifurcating periodic solutions. Finally, some numerical simulations are given to illustrate the effectiveness of our results

Research on mixed decision implications based on formal concept analysis

Decision implication is an important form of knowledge representation and acquisition in Formal Concept Analysis. Decision implication reduces the redundancy of knowledge extracted from data. However, decision implication cannot extract negative information from data, so there is information loss in decision implication. This paper introduces negative attributes to decision implication and proposes mixed decision implication, enabling decision implication to extract negative knowledge from data and to represent richer decision knowledge. This paper studies the logical systems of mixed decision implications. The semantical system of mixed decision implications is constructed to represent and deduce sound mixed decision implications and avoid contradictory mixed decision implications. In the syntactical system, Mixed Augmentation and Mixed Combination are introduced and the soundness, completeness and non-redundancy of these two inference rules are proved

Global Hopf Bifurcation Analysis for an Avian Influenza Virus Propagation Model with Nonlinear Incidence Rate and Delay

The paper investigated an avian influenza virus propagation model with nonlinear incidence rate and delay based on SIR epidemic model. We regard delay as bifurcating parameter to study the dynamical behaviors. At first, local asymptotical stability and existence of Hopf bifurcation are studied; Hopf bifurcation occurs when time delay passes through a sequence of critical values. An explicit algorithm for determining the direction of the Hopf bifurcations and stability of the bifurcation periodic solutions is derived by applying the normal form theory and center manifold theorem. What is more, the global existence of periodic solutions is established by using a global Hopf bifurcation result