Semistability of two systems of difference equations using centre manifold theory

In this paper, we study the stability of the zero equilibria of the following systems of difference equations: xn+1=axn+byne−xn,yn+1=cyn+dxne−yn and xn+1=ayn+bxne−yn,yn+1=cxn+dyne−xn where a, b, c and d are positive constants and the initial conditions x0 and y0 are positive numbers. We study the st...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical methods in the applied sciences 2016-12, Vol.39 (18), p.5216-5222
Main Authors: Psarros, N., Papaschinopoulos, G., Schinas, C. J.
Format: Article
Language:English
Subjects:
centre manifold
difference equations
semistability
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we study the stability of the zero equilibria of the following systems of difference equations: xn+1=axn+byne−xn,yn+1=cyn+dxne−yn and xn+1=ayn+bxne−yn,yn+1=cxn+dyne−xn where a, b, c and d are positive constants and the initial conditions x0 and y0 are positive numbers. We study the stability of those systems in the special case when one of the eigenvalues has absolute value equal to 1 and the other eigenvalue has absolute value less than 1, using centre manifold theory. Copyright © 2016 John Wiley & Sons, Ltd.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.3904