Open AccessAnalysis of the Fisher-KPP equation with a time-dependent Allee effect
Author(s) -
Lewa’ Alzaleq,
V. S. Manoranjan
Publication year - 2020
Publication title -
iop scinotes
Language(s) - English
Resource type - Journals
ISSN - 2633-1357
DOI - 10.1088/2633-1357/ab99cc
Subject(s) - allee effect , degenerate energy levels , fisher equation , traveling wave , mathematics , constant (computer programming) , population , riccati equation , mathematical analysis , physics , partial differential equation , computer science , economics , demography , quantum mechanics , programming language , real interest rate , sociology , monetary economics , interest rate
In this short note, we study the Fisher-KPP population model with a time-dependent Allee threshold. We consider the time dependence as sinusoidal functions and rational functions as they relate to varying environmental situations of the model. Employing the generalized Riccati equation mapping method, we obtain exact traveling wave solutions. Also, when the time-dependent Allee threshold decays to a constant value, we recover the traveling wave solution of the degenerate Fitzhugh-Nagumo equation from our general solution.