2013
DOI: 10.1080/10236198.2013.855733
|View full text |Cite
|
Sign up to set email alerts
|

Basins of attraction of equilibrium and boundary points of second-order difference equations

Abstract: Dedicated to Gerasimos Ladas on occasion of his retirement.We investigate the global behaviour of the difference equation of the formwith non-negative parameters and initial conditions such thatWe give a precise description of the basins of attraction of different equilibrium points, and show that the boundaries of the basins of attractions of different locally asymptotically stable equilibrium points or non-hyperbolic equilibrium points are in fact the global stable manifolds of neighbouring saddle or non-hyp… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
2

Citation Types

0
5
0

Year Published

2015
2015
2018
2018

Publication Types

Select...
6

Relationship

0
6

Authors

Journals

citations
Cited by 6 publications
(5 citation statements)
references
References 23 publications
0
5
0
Order By: Relevance
“…A consequence of Theorem 1 is that every bounded solution of (6) converges to either an equilibrium or a period-two solution or to a point on the boundary where the equation is not defined, see [11]. Thus the most important question becomes determining the basins of attraction of these solutions.…”
Section: Preliminariesmentioning
confidence: 96%
“…A consequence of Theorem 1 is that every bounded solution of (6) converges to either an equilibrium or a period-two solution or to a point on the boundary where the equation is not defined, see [11]. Thus the most important question becomes determining the basins of attraction of these solutions.…”
Section: Preliminariesmentioning
confidence: 96%
“…The consequence of Theorem is that every bounded solution of converges to either an equilibrium or a period‐two solution or to the point on the boundary where equation is not defined . Thus, the most important question becomes determining the basins of attraction of these solutions.…”
Section: Preliminariesmentioning
confidence: 99%
“…Equation is a special case of equations xn+1=Bxnxn1+Cxn12+Fbxnxn1+cxn12+f,n=0,1,2, and xn+1=Axn2+Bxnxn1+Cxn12+Dxn+Exn1+Faxn2+bxnxn1+cxn12+dxn+exn1+f,0.3em0.3em0.3emn=0,1,2,.... Some special cases of Eq. have been considered in the series of papers . Some special second‐order quadratic fractional difference equations have appeared in analysis of competitive and anti‐competitive systems of linear fractional difference equations in the plane .…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…We investigate the global behaviour of the equation , , 1 , 0 , Hrustić et al [13] studied the global dynamics and the bifurcations of a certain second-order rational difference equation with quadratic terms Kulenović et al [16] investigated the solutions of the difference equation Other related results on rational difference equations can be found in (([4]- [9]), [11], [14,15], [18,19], [21]).…”
Section: Introductionmentioning
confidence: 99%