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

Spectroastrometric Reverberation Mapping of Broad-line Regions

Spectroastrometry measures source astrometry as a function of wavelength/velocity. Reverberations of spectroastrometric signals naturally arise in broad-line regions (BLRs) of active galactic nuclei as a result of the continuum variations that drive responses of the broad emission lines with time delays. Such signals provide a new diagnostic for mapping BLR kinematics and geometry, complementary to the traditional intensity reverberation mapping (RM) technique. We present the generic mathematical formulism for spectroastrometric RM and show that under realistic parameters of a phenomenological BLR model, the spectroastrometric reverberation signals vary on a level of several to tens of microarcseconds, depending on the BLR size, continuum variability, and angular-size distance. We also derive the analytical expressions of spectroastrometric RM for an inclined ring-like BLR. We develop a Bayesian framework with a sophisticated Monte-Carlo sampling technique to analyze spectroastrometic data and infer the BLR properties, including the central black hole mass and angular-size distance. We demonstrate the potential of spectroastrometric RM in spatially resolving BLR kinematics and geometry through a suite of simulation tests. An application to realistic observation data of 3C~273 obtains tentative, but enlightening results, reinforcing the practical feasibility of conducting spectroastrometric RM experiments on bright AGNs with the operating Very Large Telescope Interferometer as well as possibly with the planned next-generation 30m-class telescopes.Comment: 22 pages, 17 figures, 2 tables; ApJ in press; The code BRAINS available at https://github.com/LiyrAstroph/BRAIN

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

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