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

We investigate the global behaviour of the difference equation of the form with non-negative parameters and initial conditions such that . We 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...

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Bibliographic Details
Published inJournal of difference equations and applications Vol. 20; no. 5-6; pp. 947 - 959
Main Authors Jasarevic, S, Kulenovic, MRS
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 03.06.2014
Taylor & Francis Ltd
Subjects
Asymptotic properties
Attraction
attractivity
basin
Basins
Boundaries
Boundary layer
difference equation
Difference equations
Differential equations
Equilibrium
invariant manifolds
Mathematics
Neighbouring
Saddles
stable manifold
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Summary:We investigate the global behaviour of the difference equation of the form with non-negative parameters and initial conditions such that . We 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-hyperbolic equilibrium points. Different types of bifurcations when one or more parameters are 0 are explained.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:1023-6198
1563-5120
DOI:10.1080/10236198.2013.855733