Existence and uniqueness of monotone wavefronts in a nonlocal resource-limited model

We are revisiting the topic of travelling fronts for the food-limited (FL) model with spatio-temporal nonlocal reaction. These solutions are crucial for understanding the whole model dynamics. Firstly, we prove the existence of monotone wavefronts. In difference with all previous results formulated in terms of `sufficiently small parameters', our existence theorem indicates a reasonably broad and explicit range of the model key parameters allowing the existence of monotone waves. Secondly, numerical simulations realized on the base of our analysis show appearance of non-oscillating and non-monotone travelling fronts in the FL model. These waves were never observed before. Finally, invoking a new approach developed recently by Solar $et\ al$, we prove the uniqueness (for a fixed propagation speed, up to translation) of each monotone front.Comment: 20 pages, submitte

Travelling wave solutions for Kolmogorov-type delayed lattice reaction–diffusion systems

[[abstract]]This work investigates the existence and non-existence of travelling wave solutions for Kolmogorov-type delayed lattice reaction–diffusion systems. Employing the cross iterative technique coupled with the explicit construction of upper and lower solutions in the theory of quasimonotone dynamical systems, we can find two threshold speeds c∗ and c∗ with c∗≥c∗>0. If the wave speed is greater than c∗, then we establish the existence of travelling wave solutions connecting two different equilibria. On the other hand, if the wave speed is smaller than c∗, we further prove the non-existence result of travelling wave solutions. Finally, several ecological examples including one-species, two-species and three-species models with various functional responses and time delays are presented to illustrate the analytical results.[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]SCI[[ispeerreviewed]]Y[[booktype]]紙本[[countrycodes]]GB

Traveling plane wave solutions of delayed lattice differential systems in competitive Lotka-Volterra type

99學年度楊定揮教師升等代表著作 100學年度研究獎補助論文[[abstract]]In this work we consider the existence of traveling plane wave solutions of systems of delayed lattice differential equations in competitive Lotka-Volterra type. Employing iterative method coupled with the explicit construction of upper and lower solutions in the theory of weak quasi-monotone dynamical systems, we obtain a speed, c *, and show the existence of traveling plane wave solutions connecting two different equilibria when the wave speeds are large than c *.[[incitationindex]]SCI[[booktype]]紙

2005- 2008 UNLV McNair Journal

Journal articles based on research conducted by undergraduate students in the McNair Scholars Program Table of Contents Biography of Dr. Ronald E. McNair Statements: Dr. Neal J. Smatresk, UNLV President Dr. Juanita P. Fain, Vice President of Student Affairs Dr. William W. Sullivan, Associate Vice President for Retention and Outreach Mr. Keith Rogers, Deputy Executive Director of the Center for Academic Enrichment and Outreach McNair Scholars Institute Staf

Freshwater Microplastics: Emerging Environmental Contaminants?

Emerging contaminants; Plastic pollution; Microplastic pollution; Microplastic-associated biofilms; Freshwater pollution; Inland water pollution; Plastic contaminatio