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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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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Abstract 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.
AbstractList We investigate the global behaviour of the difference equation of the form [Image omitted.]with non-negative parameters and initial conditions such that [Image omitted.]. 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 [Image omitted.] are 0 are explained.
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.
We investigate the global behaviour of the difference equation of the form ... with non-negative parameters and initial conditions such that B > 0; b + d + e + f > 0. 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 b; d; e; f are 0 are explained. (ProQuest: ... denotes formulae/symbols omitted.)
Author Jašarević, S.
Kulenović, M.R.S.
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10.1016/0022-0396(86)90086-0
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Snippet 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...
We investigate the global behaviour of the difference equation of the form ... with non-negative parameters and initial conditions such that B > 0; b + d + e +...
We investigate the global behaviour of the difference equation of the form [Image omitted.]with non-negative parameters and initial conditions such that [Image...
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SubjectTerms Asymptotic properties
Attraction
attractivity
basin
Basins
Boundaries
Boundary layer
difference equation
Difference equations
Differential equations
Equilibrium
invariant manifolds
Mathematics
Neighbouring
Saddles
stable manifold
Title Basins of attraction of equilibrium and boundary points of second-order difference equations
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