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A non-autonomous discrete commensal symbiosis model with Hassell-Varley type functional response is proposed and studied in this paper. Sufficient conditions are obtained for the existence of positive periodic solution of the system.

Population ecology theory is replete with density-dependent processes. However, trait-mediated or behavioral indirect interactions can both reinforce or oppose density-dependent effects. This paper presents the first two species competitive ODE and PDE systems, where the non-consumptive behavioral fear effect and the Allee effect, a density-dependent process, are both present. The stability of the equilibria is discussed analytically using the qualitative theory of ordinary differential equations. It is found that the Allee effect and the fear effect change the extinction dynamics of the system and the number of positive equilibrium points, but they do not affect the stability of the positive equilibria. We also observe standard co-dimension one bifurcation in the system by varying the Allee or fear parameter. Interestingly, we find that the Allee effect working in conjunction with the fear effect can bring about several dynamical changes to the system with only fear. There are three parametric regimes of interest in the fear parameter. For small and intermediate amounts of fear, the Allee + fear effect opposes dynamics driven by the fear effect. However, for large amounts of fear the Allee + fear effect reinforces the dynamics driven by the fear effect. The analysis of the corresponding spatially explicit model is also presented. To this end, the comparison principle for parabolic PDE is used. The conclusions of this paper have strong implications for conservation biology, biological control as well as the preservation of biodiversity. [ABSTRACT FROM AUTHOR]

The tensile properties of reduced activation ferritic/martensitic (RAFM) steels are significantly influenced by neutron irradiation. Here, a mechanism-based model taking account of the typical ductile damage process of void nucleation, growth, and coalescence was used to study the temperature and irradiation effects. The elastic–plastic response of RAFM steels irradiated up to 20 dpa was investigated by applying the GTN model coupled with different work hardening models. Through a numerical study of tensile curves, the GTN parameters were identified reasonably and satisfying simulation results were obtained. A combination of Swift law and Voce law was used to define the flow behavior of irradiated RAFM steels. The deformation localization could be adjusted effectively via setting the nucleation parameter εn close to the strain where necking occurs. Because εn changed with uniform elongation, εn decreased with the testing temperature and rose with an irradiation temperature above 300 °C. The nucleation parameter fn increased with the testing temperature for RAFM steels before irradiation. For irradiated RAFM steels, fn barely changed when the irradiation temperature was below 300 °C and then it rose at a higher irradiation temperature. Meanwhile, the ultimate strength of the simulated and experimental curves showed good agreement, indicating that this method can be applied to engineering design. [ABSTRACT FROM AUTHOR]

We propose and study a class of discrete-time commensalism systems with additive Allee effects on the host species. First, the single species with additive Allee effects is analyzed for existence and stability, then the existence of fixed points of discrete systems is given, and the local stability of fixed points is given by characteristic root analysis. Second, we used the center manifold theorem and bifurcation theory to study the bifurcation of a codimension of one of the system at non-hyperbolic fixed points, including flip, transcritical, pitchfork, and fold bifurcations. Furthermore, this paper used the hybrid chaos method to control the chaos that occurs in the flip bifurcation of the system. Finally, the analysis conclusions were verified by numerical simulations. Compared with the continuous system, the similarities are that both species' densities decrease with increasing Allee values under the weak Allee effect and that the host species hastens extinction under the strong Allee effect. Further, when the birth rate of the benefited species is low and the time is large enough, the benefited species will be locally asymptotically stabilized. Thus, our new finding is that both strong and weak Allee effects contribute to the stability of the benefited species under certain conditions. [ABSTRACT FROM AUTHOR]