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This article investigates a class of Duffing nonlinear dynamic systems with fractional‐order dry friction and conducts in‐depth research on the stability, chaotic characteristics, and erosion of the safety basin of this system; the results are verified through numerical simulation. First, the average method is used to approximate the amplitude–frequency relationship of the system, and the accuracy of the analytical results is verified through numerical experiments. Second, the Melnikov method is used to obtain the conditions for the system to enter chaos in the Smale horseshoe sense, and the Melnikov curve is drawn for further verification. Then, bifurcation diagrams are drawn for the changes in various parameters in the system, with a focus on analyzing the influence of friction factors on chaotic bifurcation. By applying the definition and calculation principle of the maximum Lyapunov exponent, and drawing and utilizing the maximum Lyapunov exponent graph, the chaotic state that the system enters under different parameters is more clearly defined. Finally, the evolution law of the safety basin under various parameter changes, especially dry friction changes, is analyzed, and the erosion and bifurcation mechanism of the safety basin is studied. Comparing with the bifurcation diagram, it reveals that chaos primarily contributes to the erosion of the safety basin. [ABSTRACT FROM AUTHOR]

Hyperuricemia has evolved into a global public health concern, and applying probiotics fermented apple juice holds promise for alleviating this condition. This study aimed to investigate the biotransformation and metabolic features of urate-lowering probiotics sequentially fermented dealcoholized apple juice (PSFA), and assess its ameliorative effects and potential mechanisms on hyperuricemia mice. Results showed that CICC 6074 and 20,292 possessed excellent purine, nucleotide and nucleoside degradation and acid and bile salt resistance; sequential fermentation decreased the fructose in apple juice, and viable counts reached 3.76 × 108 CFU/mL. Histopathological analysis showed that PSFA ameliorated kidney damage in hyperuricemia mice. Furthermore, PSFA significantly reduced Urea, Creatinine and Uric acid levels in hyperuricemia mice; and inhibited xanthine oxidase activity and the expression of pro-inflammatory factors. Importantly, PSFA reversed gut microbiota dysbiosis and raised the abundance of beneficial bacteria (Lactobacillush , Faecalibaculum and Lachnospiraceae_NK4A136_group). KEGG and COG functional prediction results revealed that the potential mechanism of PSFA to ameliorate hyperuricemia may be lipid metabolism and glycolysis pathways. [Display omitted] • CICC 6064 and CICC 20292 exhibit favorable fermentation performance and uric acid degradation ability. • Mixed bacterial fermentation enriched the nutrients and volatile substances of apple juice. • PSFA increased beneficial microbiota Lactobacillush , Faecalibaculum and Lachnospiraceae_NK4A136_ group. • Lipid metabolism and glycolysis pathways play pivotal roles in mitigating hyperuricemia. [ABSTRACT FROM AUTHOR]

This article investigates the chaotic analysis and attractive domain of a fractional‐order Φ6$$ {\Phi}^6 $$‐van der Pol with time delay velocity under harmonic excitation. Firstly, eight different types of bifurcation states of the system under different parameters are calculated by using the undisturbed system. Secondly, the Melnikov method is used to explore the effect of time delay velocity on the threshold of chaos in the Smale horseshoe sense under the double‐well potential and three‐well potential of the system. Finally, through numerical analysis of the phase diagram, bifurcation diagram, and maximum Lyapunov exponent, the influence of time delay velocity on system chaos is studied. The results indicate that an increase in the delay velocity coefficient will lead to the system transitioning from a chaotic state to a periodic state, while an increase in the delay velocity term will lead to the system transitioning from a periodic state to a chaotic state. In the study of system bifurcation, it is found that the position of the equilibrium points of the system changes during periodic motion. Therefore, cell mapping is used to draw the attractive domain of the system is studying the influence of initial conditions on the equilibrium point of the system and the results show that there is a close relationship between the attraction domain and the process of chaos occurrence. [ABSTRACT FROM AUTHOR]