Persistence of solutions in a nonlocal predator-prey system with a shifting habitat

In this paper, we mainly study the propagation properties of a nonlocal dispersal predator-prey system in a shifting environment. It is known that Choi et al. [J. Differ. Equ. 302 (2021), pp. 807-853] studied the persistence or extinction of the prey and the predator separately in various moving frames. In particular, they achieved a complete picture in the local diffusion case. However, the question of the persistence of the prey and the predator in some intermediate moving frames in the nonlocal diffusion case is left open in Choi et al.'s paper. By using some prior estimates, the Arzela-Ascoli theorem and a diagonal extraction process, we can extend and improve the main results of Choi et al. to achieve a complete picture in the nonlocal diffusion case

6-(4-Nitro­benz­yloxy)quinoline

In the mol­ecule of the title compound, C16H12N2O3, the nitrobenzene benzene ring forms a dihedral angle of 23.8 (8)° with the plane of the quinoline ring system. The crystal structure is stabilized by an aromatic π–π stacking inter­action between centrosymmetrically related benzene rings [centroid–centroid distance 3.663 (2) Å]

Traveling Wave in a Ratio-dependent Holling-Tanner System with Nonlocal Diffusion and Strong Allee Effect

In this paper, a ratio-dependent Holling-Tanner system with nonlocal diffusion is taken into account, where the prey is subject to a strong Allee effect. To be special, by applying Schauder's fixed point theorem and iterative technique, we provide a general theory on the existence of traveling waves for such system. Then appropriate upper and lower solutions and a novel sequence, similar to squeeze method, are constructed to demonstrate the existence of traveling waves for c>c*. Moreover, the existence of traveling wave for c=c* is also established by spreading speed theory and comparison principle. Finally, the nonexistence of traveling waves for c<c* is investigated, and the minimal wave speed then is determined

A sufficient condition on successful invasion by the predator

In this paper, we provide a sufficient condition on successful invasion by the predator. Specially, we obtain the persistence of traveling wave solutions of predator-prey system, in which the predator can survive without the predation of the prey. This proof heavily depends on comparison principle of scalar monostable equation, the rescaling method and phase-plane analysis

Traveling Waves of Modified Leslie-Gower Predator-prey Systems

The spreading phenomena in modified Leslie-Gower reaction-diffusion predator-prey systems are the topic of this paper. We mainly study the existence of two different types of traveling waves. Be specific, with the aid of the upper and lower solutions method, we establish the existence of traveling wave connecting the prey-present state and the coexistence state or the prey-present state and the prey-free state by constructing different and appropriate Lyapunov functions. Moreover, for traveling wave connecting the prey-present state and the prey-free state, we gain more monotonicity information on wave profile based on the asymptotic behavior at negative infinite. Finally, our results are applied to modified Leslie-Gower system with Holling II type or Lotka-Volterra type, and then a novel Lyapunov function is constructed for the latter, which further enhances our results. Meanwhile, some numerical simulations are carried to support our results

{Bis[2-(dicyclo­hexyl­phosphino)phen­yl]methyl­silyl-κ3 P,Si,P′}chloridoplatinum(II)

In the title compound, [Pt(C37H55P2Si)Cl], prepared from MeSiH[(cy)2PC6H4]2 and [Pt(cod)Cl2] (cy = cyclo­hexyl; cod = cyclo­octa-1,5-diene), the PtII atom is coordinated by two P atoms, one Si atom and one Cl atom in a distorted square-planar geometry. The two P atoms are in a trans arrangement and the four cyclo­hexane rings adopt a chair conformation

{Bis[2-(dicyclo­hexyl­phosphino)­phen­yl]methyl­silyl-κ3 P,Si,P′}chloridopalladium(II)

In the title compound, [Pd(C37H55P2Si)Cl], the Pd atom has a distorted square-planar geometry. The two five-membered rings adopt envelope conformations, while the four cyclo­hexane rings have chair conformations. The two planar aromatic rings are oriented at a dihedral angle of 28.79 (3)°

Bis(4-fluoro­anilinium) tetra­chloridocuprate(II)

The crystal structure of the title compound, (C6H7FN)2[CuCl4], consists of parallel two-dimensional perovskite-type layers of corner-sharing CuCl6 octa­hedra. These are bonded together via N—H⋯Cl hydrogen bonds from the 4-fluoro­anilinium chains, which are almost perpendicular to the layers. The CuCl4 dianions have two short Cu—Cl bonds [2.2657 (15) and 2.2884 (13) Å] and two longer bonds [2.8868 (15) Å], giving highly Jahn–Teller-distorted CuCl6 octa­hedra. The Cu atoms are situated on crystallographic centers of inversion