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In this article, the general Liénard system dxdt=ϕ(y)−F(x),dydt=−g(x)\left\{\begin{array}{l}\frac{{\rm{d}}x}{{\rm{d}}t}=\phi (y)-F\left(x),\\ \frac{{\rm{d}}y}{{\rm{d}}t}=-g\left(x)\end{array}\right. is studied. By using the Filippov transformation, combined with the careful estimation of divergence along the closed orbit, we prove the sufficient conditions for the uniqueness of limit cycles in this system. Our results extend almost all the related existing studies on the Liénard system.

In order to obtain the optimal technological parameters of lettuce vacuum osmotic dehydration, the effects of osmotic temperature, slice thickness, sucrose concentration, and vacuum degree on the vacuum osmotic dehydration were explored. The lettuce water loss rate and solid gain rate decreased with the increase of slice thickness and vacuum degree, and increased with the increase of sucrose concentration and osmotic temperature. Response surface methodology was applied to analyze the influence of the four influential factors on the evaluated parameters and the optimization of lettuce vacuum osmotic dehydration was studied. The results indicated that, within the experimental scope, the optimized technological parameters of lettuce vacuum osmotic dehydration are the temperature of 28°C, the slice thickness of 2 mm, sucrose concentration of 47%, the vacuum degree of 22 kPa, and the water loss rate and solid gain rate are 72.16% and 11.82%, respectively.

In order to reveal the change laws of microstructure in apple slices during hot air‐explosion puffing drying, the microstructure images and parameters of apple slices under different drying conditions were obtained by using paraffin sectioning, microscopic observation, and image processing techniques with apples as raw material and CO2 as drying medium. Subsequently, the changes in internal cell and pore structure of dried apple slices were analyzed, as well as the relationship between micro‐parameters of apple slices and macro‐measurement indicators was further obtained. Results indicated that the overall cross‐sectional area, cross‐sectional perimeter, equivalent diameter, and porosity of cells increased by explosion puffing drying, while the cell roundness and wall roughness factors changed relatively little. Meanwhile, macro–micro parameters of expanded apples were fitted and analyzed. Then, the obtained mathematical model showed a nonlinear correlation as experimental and predicted results exhibited good agreement, with determination coefficients R2 more significant than 0.8, which could better expect the macro–microparameters to change in the drying process. The results of this research could provide an essential reference for exploring the change laws of tissue microstructure parameters in apples dried by hot air‐explosion puffing drying, with expansion and rehydration ratios under different experimental conditions, as well as optimizing the puffing drying process and designing corresponding drying equipment. Practical Applications: Fresh apples have high moisture content and are not easy to store, so drying is usually used to reduce the moisture content to extend shelf time and increase economic benefits. For the drying process of fruit and vegetable products, scholars mainly focused on the influence of microstructure parameters on moisture migration, drying rate, heat and mass transfer and other factors, but did not give a quantitative description of how microstructure parameters affect macroscopic parameters. In this article, the relationship between microstructural changes and macroscopic indicators was investigated by taking puffed apple slices as an example. Research could provide an essential reference for exploring the change laws of tissue microstructure parameters in apples dried by hot air‐explosion puffing drying, with expansion and rehydration ratios under different experimental conditions, as well as optimizing the puffing drying process and designing corresponding drying equipment. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonlocal population model with stage structure in an unbounded domain. Using a fluctuation method and the compact open topology, a threshold dynamics and global attractivity of positive steady state are established. And the main results extend the related existing studies on the nonlocal population model. [ABSTRACT FROM AUTHOR]

In order to obtain the optimized technological parameters of hot air-vacuum combined drying of lettuce, the effects of hot air temperature, intermediate conversion moisture content, slice thickness and vacuum degree (four influence factors) on lettuce drying were explored. The drying time and rehydration ratio of lettuce were the experimental indices, and the relationships between the experimental indices and the influence factors were analyzed by using the response surface methodology. The regression mathematical models were established. The optimized technological parameters of hot air and vacuum combined drying are 50C hot air temperature, 40% intermediate conversion moisture content (w.b.), 20 kPa vacuum degree and 5 mm slice thickness. Practical Applications Combined drying is widely used in food, which is considered as an effective method to achieve energy conservation and shelf life. The objective of this paper was using response surface methodology to obtain optimized hot air vacuum drying parameters for lettuce. The significance of this research can improve the drying efficiency, provide a reference for other fruits and vegetables' drying process optimization and provide a technical basis for the drying of lettuce and the designing of related equipment. [ABSTRACT FROM AUTHOR]