Minimal wave speed of a competition integrodifference system

2018 ◽  
Vol 24 (6) ◽  
pp. 941-954 ◽  
Author(s):  
Luping Li ◽  
Shugui Kang ◽  
Lili Kong ◽  
Huiqin Chen
Keyword(s):  
Wave Speed ◽  
Minimal Wave Speed

scholarly journals Minimal Wave Speed in a Predator-Prey System with Distributed Time Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Fuzhen Wu ◽  
Dongfeng Li
Keyword(s):  
Time Delay ◽  
Traveling Wave ◽  
Wave Speed ◽  
Upper And Lower Solutions ◽  
Traveling Wave Solutions ◽  
Predator Prey ◽  
Wave Solutions ◽  
Prey System ◽  
Minimal Wave Speed ◽  
Distributed Time Delay

This paper is concerned with the minimal wave speed of traveling wave solutions in a predator-prey system with distributed time delay, which does not satisfy comparison principle due to delayed intraspecific terms. By constructing upper and lower solutions, we obtain the existence of traveling wave solutions when the wave speed is the minimal wave speed. Our results complete the known conclusions and show the precisely asymptotic behavior of traveling wave solutions.

Minimal wave speed of a diffusive SIR epidemic model with nonlocal delay

2019 ◽  
Vol 12 (07) ◽  
pp. 1950081
Author(s):  
Fuzhen Wu ◽  
Dongfeng Li
Keyword(s):  
Traveling Wave ◽  
Epidemic Model ◽  
Wave Speed ◽  
Traveling Wave Solutions ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Nonlocal Delay ◽  
Spatial Nonlocality ◽  
Wave Solutions ◽  
Minimal Wave Speed

This paper is concerned with the minimal wave speed in a diffusive epidemic model with nonlocal delays. We define a threshold. By presenting the existence and the nonexistence of traveling wave solutions for all positive wave speed, we confirm that the threshold is the minimal wave speed of traveling wave solutions, which models that the infective invades the habitat of the susceptible. For some cases, it is proven that spatial nonlocality may increase the propagation threshold while time delay decreases the threshold.

Selection mechanism of the minimal wave speed to the Lotka–Volterra competition model

2020 ◽  
Vol 104 ◽  
pp. 106281
Author(s):  
Manjun Ma ◽  
Dong Chen ◽  
Jiajun Yue ◽  
Yazhou Han
Keyword(s):  
Wave Speed ◽  
Competition Model ◽  
Selection Mechanism ◽  
Minimal Wave Speed

scholarly journals Existence of Traveling Wave Solutions for Cholera Model

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Tianran Zhang ◽  
Qingming Gou ◽  
Xiaoli Wang
Keyword(s):  
Traveling Wave ◽  
Wave Speed ◽  
Shooting Method ◽  
Reproduction Number ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Traveling Wave Solution ◽  
Reaction Diffusion Model ◽  
Minimal Wave Speed ◽  
The Basic Reproduction Number

To investigate the spreading speed of cholera, Codeço’s cholera model (2001) is developed by a reaction-diffusion model that incorporates both indirect environment-to-human and direct human-to-human transmissions and the pathogen diffusion. The two transmission incidences are supposed to be saturated with infective density and pathogen density. The basic reproduction numberR0is defined and the formula for minimal wave speedc*is given. It is proved by shooting method that there exists a traveling wave solution with speedcfor cholera model if and only ifc≥c*.

scholarly journals The Minimal Wave Speed of a Lotka-Volterra Competition Model

2021 ◽  
Vol 42 (6) ◽  
pp. 575-585
Author(s):  
ZHANG Yafei ◽  
◽  
◽  
ZHOU Yinbo
Keyword(s):  
Wave Speed ◽  
Competition Model ◽  
Minimal Wave Speed

Traveling wave solutions in predator–prey models with competition

2021 ◽  
Author(s):  
Guo Lin ◽  
Yibing Xing
Keyword(s):  
Traveling Wave ◽  
Wave Speed ◽  
Traveling Wave Solutions ◽  
Initial Value ◽  
Predator Prey ◽  
Wave Solutions ◽  
Minimal Wave Speed ◽  
Predator Prey Models ◽  
Scalar Equations ◽  
Asymptotic Spreading

This paper studies the minimal wave speed of traveling wave solutions in predator–prey models, in which there are several groups of predators that compete among different groups. We investigate the existence and nonexistence of traveling wave solutions modeling the invasion of predators and coexistence of these species. When the positive solution of the corresponding kinetic system converges to the unique positive steady state, a threshold that is the minimal wave speed of traveling wave solutions is obtained. To finish the proof, we construct contracting rectangles and upper–lower solutions and apply the asymptotic spreading theory of scalar equations. Moreover, multiple propagation thresholds in the corresponding initial value problem are presented by numerical examples, and one threshold may be the minimal wave speed of traveling wave solutions.

SPREAD RATES UNDER TEMPORAL VARIABILITY: CALCULATION AND APPLICATION TO BIOLOGICAL INVASIONS

2011 ◽  
Vol 21 (12) ◽  
pp. 2469-2489 ◽  
Author(s):  
GUNOG SEO ◽  
FRITHJOF LUTSCHER
Keyword(s):  
Biological Invasions ◽  
Temporal Variability ◽  
Life Histories ◽  
Wave Speed ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Reaction Diffusion Equation ◽  
Coefficient Function ◽  
Compartment System ◽  
Minimal Wave Speed

In this paper, we introduce a technique to study the minimal wave speed in reaction-diffusion equations with temporal variability and apply it to two particular models for biological invasions. We use the exponential transform to avoid solving partial differential equations explicitly or finding inverse transforms. In a single reaction-diffusion equation with time-periodic coefficients, the minimal wave speed depends only on time-averages of each coefficient function. In a two-compartment system with mobile and stationary individuals, the invasion speed depends on the precise form of the coefficient functions and their temporal correlations; in some cases, a lower bound can be obtained. Our technique can be extended to more complex life histories of invading organisms.

Minimal wave speed of a competitive integrodifference system

2019 ◽  
Vol 12 (03) ◽  
pp. 1950031
Author(s):  
Fuguo Zhu ◽  
Shuxia Pan
Keyword(s):  
Traveling Wave ◽  
Wave Speed ◽  
Upper And Lower Solutions ◽  
Traveling Wave Solutions ◽  
Competitive System ◽  
Volterra Type ◽  
Wave Solutions ◽  
Minimal Wave Speed

This paper is concerned with the minimal wave speed of traveling wave solutions of a discrete competitive system with Lotka–Volterra type nonlinearity. By constructing upper and lower solutions, we confirm the existence of traveling wave solutions if the wave speed is the minimal wave speed. Our results complete the earlier conclusions.

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