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A diffusive predator-prey system with both the additive Allee effect and the fear effect in the prey subject to Neumann boundary conditions is considered in this paper. Firstly, non-negative and non-trivial solution a priori estimations are shown. Furthermore, for specific parameter ranges, the absence of non-constant positive solutions is demonstrated. Secondly, we use the linearized theory to investigate the stability of non-negative constant solutions. The spatially homogeneous and non-homogeneous periodic solutions, as well as non-constant steady state solutions, are next investigated by using Allee effect parameters as the bifurcation parameter. Finally, numerical simulation is used to illustrate some theoretical results.

The existence and approximation of manifolds for the Swift-Hohenberg equation with a proper parameter have mainly been studied. Using the backward-forward systems from Swift-Hohenberg equation, the existence and specific representation forms of manifolds for Swift-Hohenberg equation with a parameter have been obtained. Meanwhile, we make use of technique of deposition of lower and higher frequency spaces of solutions and assume the reduced system to obtain the main numeration approximation system of approximation solution for the original system Swift-Hohenberg equation with a proper parameter.

In this paper, the existence of random attractors for nonautonomous stochastic reversible Selkov system with multiplicative noise has been proved through Ornstein-Uhlenbeck transformation. Furthermore, the upper semicontinuity of random attractors is discussed when the intensity of noise approaches zero. The main difficulty is to prove the asymptotic compactness for establishing the existence of tempered pullback random attractor.

Honeycomb paperboard is a kind of environmental-friendly package cushioning material with honeycomb sandwich structure, and may be employed to protect products from shock or vibration damage during distribution. This paper deals with the characterization of properties of honeycomb paperboard relevant to its application for protective packaging in transportation, such as dynamic cushion curves and vibration transmissibility. The main feature of the paper is the evaluation on the shock absorbing characteristics and vibration transmissibility of honeycomb paperboards with different thickness by a series of experimental studies on the drop shock machine and vibration table. By using the fitting polynomial of the curve, the experiential formulas and characteristic coefficients of dynamic cushion curves of honeycomb paperboards with different thickness have been obtained. From the vibration tests with slow sine sweep, the peak frequencies and vibration transmissibility are measured and used to estimate the damping ratios. All the works provide basic data and curves relevant to its application for protective packaging in transportation.