scholarly journals Existence and stability of travelling wave solutions of competition models: A degree theoretic approach

1982 ◽  
Vol 44 (3) ◽  
pp. 343-364 ◽  
Author(s):  
Robert A. Gardner
Keyword(s):  
Travelling Wave ◽  
Theoretic Approach ◽  
Travelling Wave Solutions ◽  
Competition Models ◽  
Wave Solutions ◽  
Existence And Stability

Existence and stability of non-monotone travelling wave solutions for the diffusive Lotka–Volterra system of three competing species

Nonlinearity ◽  
2020 ◽  
Vol 33 (10) ◽  
pp. 5080-5110 ◽  
Author(s):  
Chueh-Hsin Chang ◽  
Chiun-Chuan Chen ◽  
Li-Chang Hung ◽  
Masayasu Mimura ◽  
Toshiyuki Ogawa
Keyword(s):  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Volterra System ◽  
Competing Species ◽  
Wave Solutions ◽  
Existence And Stability

scholarly journals TRAVELLING WAVE SOLUTIONS IN NONLOCAL REACTION–DIFFUSION SYSTEMS WITH DELAYS AND APPLICATIONS

2009 ◽  
Vol 51 (1) ◽  
pp. 49-66 ◽  
Author(s):  
ZHI-XIAN YU ◽  
RONG YUAN
Keyword(s):  
Reaction Diffusion ◽  
Travelling Wave ◽  
Accurate Information ◽  
Travelling Wave Solutions ◽  
Reaction Diffusion Systems ◽  
Competition Models ◽  
Wave Solutions ◽  
Diffusion Systems ◽  
Nonlocal Reaction ◽  
Iteration Technique

AbstractThis paper deals with two-species convolution diffusion-competition models of Lotka–Volterra type with delays which describe more accurate information than the Laplacian diffusion-competition models. We first investigate the existence of travelling wave solutions of a class of nonlocal convolution diffusion systems with weak quasimonotonicity or weak exponential quasimonotonicity by a cross-iteration technique and Schauder’s fixed point theorem. When the results are applied to the convolution diffusion-competition models with delays, we establish the existence of travelling wave solutions as well as asymptotic behaviour.

Existence and stability of travelling wave solutions for an evolutionary ecology model

1990 ◽  
Vol 115 (1-2) ◽  
pp. 1-18 ◽  
Author(s):  
Roger Lui
Keyword(s):  
Population Size ◽  
Evolutionary Ecology ◽  
Reaction Diffusion ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Fisher’S Equation ◽  
Wave Solutions ◽  
Fisher's Equation ◽  
Existence And Stability ◽  
The Stability

SynopsisMonotone travelling wave solutions are known to exist for Fisher's equation which models the propagation of an advantageous gene in a single locus, two alleles population genetics model. Fisher's equation assumed that the population size is a constant and that the fitnesses of the individuals in the population depend only on their genotypes. In this paper, we relax these assumptions and allow the fitnesses to depend also on the population size. Under certain assumptions, we prove that in the second heterozygote intermediate case, there exists a constant θ*>0 such that monotone travelling wave solutions for the reaction–diffusion system exist whenever θ > θ*. We also discuss the stability properties of these waves.

Solitary and Travelling Wave Solutions of Certain Nonlinear Diffusion-Reaction Equations

2020 ◽  
Author(s):  
Miftachul Hadi
Keyword(s):  
Nonlinear Diffusion ◽  
Travelling Wave ◽  
Diffusion Reaction ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Reaction Equations

We review the work of Ranjit Kumar, R S Kaushal, Awadhesh Prasad. The work is still in progress.

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