Bifurcations in a delay logistic equation under small perturbations
type: Item
instance of: scholarly article
title: Bifurcations in a delay logistic equation under small perturbations
zbMATH Open document ID: 1472.34133
DOI: 10.3103/S1066369X20100059
published in: Russian Mathematics
publication date: 2021-05-28T00:00:00Z
review text: Consider the following equation, known as the delay logistic equation, \[ \frac{du}{dt}=\lambda \big[ 1-u(t-T)\big] u \quad (\lambda >0, \ T>0), \] which is encountered in mathematical ecology, physics, etc. In the first part of the paper, the local behavior of solutions to the above equation is analyzed by using bifurcation methods. In particular, the author studies the dependence of dynamic properties of solutions on small perturbations of the above equation that contain a large delay \(h>0\). The second part of the paper is devoted to the delay logistic equation with periodic perturbations of parameters. Using standard asymptotic methods the parametric resonance is deduced under a two-frequency perturbation.
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 34K27
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 7351956
zbMATH Keywords: bifurcation
zbMATH Keywords: asymptotics
zbMATH Keywords: parametric resonance
author: S. A. Kashchenko
reviewed by: Gheorghe Moroşanu
MaRDI profile type: Publication
cites work: A non-linear difference-differential equation.
cites work: Q3251626
cites work: The existence of periodic solutions of \(f'(x)=-\alpha f(x-1)(1+f(x))\)
cites work: Delay differential equations: with applications in population dynamics
cites work: Nonlocality of reaction-diffusion equations induced by delay: biological modeling and nonlinear dynamics
cites work: Theory of functional differential equations. 2nd ed
cites work: Theory and applications of partial functional differential equations
cites work: Q4138551
cites work: Q4429919
cites work: Mathematical biology. Vol. 2: Spatial models and biomedical applications.
cites work: Q4318853
cites work: Applied Delay Differential Equations
cites work: Bifurcations in the neighborhood of a cycle under small perturbations with a large delay
cites work: BIFURCATIONAL FEATURES IN SYSTEMS OF NONLINEAR PARABOLIC EQUATIONS WITH WEAK DIFFUSION
cites work: Q4204477
cites work: The Ginzburg-Landau equation as a normal form for a second-order difference-differential equation with a large delay
cites work: Q5213005
cites work: Q3892547
cites work: Q3900378
cites work: Q2951867
cites work: Q3992468
cites work: Q4139051
full work available at URL: s1066369x20100059
OpenAlex ID: W3101296278
description: scientific article; zbMATH DE number 7351956