This paper concerned with a diffusive predator–prey model with fear effect. First, some basic dynamics of system is analyzed. Then based on stability analysis, we derive some conditions for stability and bifurcation of constant steady state. Furthermore, we derive some results on the existence and nonexistence of nonconstant steady states of this model by considering the effect of diffusion. Finally, we present some numerical simulations to verify our theoretical results. By mathematical and numerical analyses, we find that the fear can prevent the occurrence of limit cycle oscillation and increase the stability of the system, and the diffusion can also induce the chaos in the system.
more »
« less
Near-sunflowers and focal families
We present some problems and results about variants of sunflowers in families of sets. In particular, we improve an upper bound of the first author, Körner and Monti on the maximum number of binary vectors of length n so that every four of them are split into two pairs by some coordinate. We also propose a weaker version of the Erdős-Rado sunflower conjecture.
more »
« less
- Award ID(s):
- 2154082
- NSF-PAR ID:
- 10498649
- Publisher / Repository:
- Springer Link
- Date Published:
- Journal Name:
- Israel Journal of Mathematics
- Volume:
- 256
- Issue:
- 1
- ISSN:
- 0021-2172
- Page Range / eLocation ID:
- 21 to 33
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
As members of the editorial team at Language Acquisition, we read Kidd and Garcia’s target article with enthusiasm. In our commentary, we outline some specific ideas for how journals can help to alleviate the issues raised by Kidd and Garcia, some of which are in progress or in place at Language Acquisition, and some of which we hope to undertake alongside other journals in the field. We focus on concrete steps, acknowledging that systemic changes, too, will be required to ensure that our science reflects the diversity of languages learned.more » « less
-
In this paper, we discuss some of the key challenges in the study of time-dependent processes and non-equilibrium behaviour in warm dense matter. We outline some of the basic physics concepts that have underpinned the definition of warm dense matter as a subject area in its own right and then cover, in a selective, non-comprehensive manner, some of the current challenges, pointing along the way to topics covered by the papers presented in this volume. This article is part of the theme issue ‘Dynamic and transient processes in warm dense matter’.more » « less
-
more » « less
Abstract In this work we give some maximal inequalities in Triebel–Lizorkin spaces, which are “
‐variants” of Fefferman–Stein vector‐valued maximal inequality and Peetre's maximal inequality. We will give some applications of the new maximal inequalities and discuss sharpness of some results. -
We review the existing literature concerning regularity for the gradient of weak solutions of the subelliptic p-Laplacian differential operator in a domain Ω in the Heisenberg group H^n, with 1 ≤ p < ∞, and of its parabolic counterpart. We present some open problems and outline some of the difficulties they present.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/S11856-023-2500-1
