Minimal-speed selection of traveling waves to the Lotka–Volterra competition model

2019 ◽  
Vol 266 (11) ◽  
pp. 7357-7378 ◽  
Author(s):  
Ahmad Alhasanat ◽  
Chunhua Ou
Keyword(s):  
Traveling Waves ◽  
Competition Model ◽  
Minimal Speed ◽  
Speed Selection ◽  
Selection Of

scholarly journals Speed determinacy of the traveling waves for a three species time-periodic Lotka-Volterra competition system

2021 ◽  
Author(s):  
Qiong Wu ◽  
Chaohong Pan ◽  
Hongyong Wang
Keyword(s):  
Traveling Waves ◽  
Upper And Lower Solutions ◽  
Sufficient Conditions ◽  
Lower Solution ◽  
Competition System ◽  
Periodic Traveling Waves ◽  
Minimal Wave Speed ◽  
Speed Selection ◽  
Time Periodic ◽  
Selection Of

In this paper, speed selection of the time periodic traveling waves for a three species time-periodic Lotka-Volterra competition system is studied via the upper-lower solution method as well as the comparison principle. Through constructing specific types of upper and lower solutions to the system, the speed selection of the minimal wave speed can be determined under some sets of sufficient conditions composed of the parameters in the system.

scholarly journals Hyperbolic traveling waves driven by growth

2014 ◽  
Vol 24 (06) ◽  
pp. 1165-1195 ◽  
Author(s):  
Emeric Bouin ◽  
Vincent Calvez ◽  
Grégoire Nadin
Keyword(s):  
Nonlinear Stability ◽  
Traveling Waves ◽  
Hyperbolic Model ◽  
Kpp Equation ◽  
Transition Parameter ◽  
Minimal Speed ◽  
Traveling Fronts ◽  
Traveling Front ◽  
Maximal Speed ◽  
Existence And Stability

We perform the analysis of a hyperbolic model which is the analog of the Fisher-KPP equation. This model accounts for particles that move at maximal speed ϵ-1 (ϵ > 0), and proliferate according to a reaction term of monostable type. We study the existence and stability of traveling fronts. We exhibit a transition depending on the parameter ϵ: for small ϵ the behavior is essentially the same as for the diffusive Fisher-KPP equation. However, for large ϵ the traveling front with minimal speed is discontinuous and travels at the maximal speed ϵ-1. The traveling fronts with minimal speed are linearly stable in weighted L2 spaces. We also prove local nonlinear stability of the traveling front with minimal speed when ϵ is smaller than the transition parameter.

scholarly journals Monotone traveling waves for delayed neural field equations

2016 ◽  
Vol 26 (10) ◽  
pp. 1919-1954 ◽  
Author(s):  
Jian Fang ◽  
Grégory Faye
Keyword(s):  
Traveling Waves ◽  
Traveling Wave ◽  
Level Sets ◽  
Single Layer ◽  
Traveling Wave Solutions ◽  
Neural Field ◽  
Field Equations ◽  
Minimal Speed ◽  
Wave Solutions ◽  
Neural Field Equations

We study the existence of traveling wave solutions and spreading properties for single-layer delayed neural field equations. We focus on the case where the kinetic dynamics are of monostable type and characterize the invasion speeds as a function of the asymptotic decay of the connectivity kernel. More precisely, we show that for exponentially bounded kernels the minimal speed of traveling waves exists and coincides with the spreading speed, which further can be explicitly characterized under a KPP type condition. We also investigate the case of algebraically decaying kernels where we prove the non-existence of traveling wave solutions and show the level sets of the solutions eventually locate in-between two exponential functions of time. The uniqueness of traveling waves modulo translation is also obtained.

DIFFUSION-DRIVEN INSTABILITY AND WAVE PATTERNS OF LESLIE–GOWER COMPETITION MODEL

2015 ◽  
Vol 23 (03) ◽  
pp. 385-399
Author(s):  
MEI-FENG LI ◽  
GUANG ZHANG ◽  
ZHI-YI LU ◽  
LU ZHANG
Keyword(s):  
Fixed Point ◽  
Traveling Waves ◽  
Diffusion Coefficients ◽  
Periodic Boundary ◽  
Competitive Exclusion ◽  
Periodic Boundary Conditions ◽  
Linearization Method ◽  
Competition Model ◽  
Inner Product ◽  
Wave Patterns

In this paper, the diffusion-driven instability of the Leslie–Gower competition model with the periodic boundary conditions is investigated. By using the linearization method and the inner product techniques, the instability conditions of this model at the coexistence fixed point and the competitive exclusion fixed points are obtained, respectively. As an example, the diffusion-driven instability conditions of a symmetric Leslie–Gower competition model at the coexistence fixed point is obtained when the diffusion coefficients are equal. Under these instability conditions, various patterns, including spirals, traveling waves and disorders, are observed in the numerical simulations. On the other hand, we also numerically investigate the effects of diffusion coefficient and the strength of the interspecific competition on the wave patterns.

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