Periodic and Chaotic Orbits of a Discrete Rational System
We study a rational planar system consisting of one linear-affine and one linear-fractional difference equation. If all of the system’s parameters are positive (so that the positive quadrant is invariant and the system is continuous), then we show that the unique fixed point of the system in the pos...
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| Format: | Article |
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Hindawi Limited
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/519598 |
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doaj-ad402ce68b564dee8cc6ab65d57539772020-11-24T21:04:22ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/519598519598Periodic and Chaotic Orbits of a Discrete Rational SystemN. Lazaryan0H. Sedaghat1Department of Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014, USADepartment of Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014, USAWe study a rational planar system consisting of one linear-affine and one linear-fractional difference equation. If all of the system’s parameters are positive (so that the positive quadrant is invariant and the system is continuous), then we show that the unique fixed point of the system in the positive quadrant cannot be repelling and the system does not have a snap-back repeller. By folding the system into a second-order equation, we find special cases of the system with some negative parameter values that do exhibit chaos in the sense of Li and Yorke within the positive quadrant of the plane.http://dx.doi.org/10.1155/2015/519598 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
N. Lazaryan H. Sedaghat |
| spellingShingle |
N. Lazaryan H. Sedaghat Periodic and Chaotic Orbits of a Discrete Rational System Discrete Dynamics in Nature and Society |
| author_facet |
N. Lazaryan H. Sedaghat |
| author_sort |
N. Lazaryan |
| title |
Periodic and Chaotic Orbits of a Discrete Rational System |
| title_short |
Periodic and Chaotic Orbits of a Discrete Rational System |
| title_full |
Periodic and Chaotic Orbits of a Discrete Rational System |
| title_fullStr |
Periodic and Chaotic Orbits of a Discrete Rational System |
| title_full_unstemmed |
Periodic and Chaotic Orbits of a Discrete Rational System |
| title_sort |
periodic and chaotic orbits of a discrete rational system |
| publisher |
Hindawi Limited |
| series |
Discrete Dynamics in Nature and Society |
| issn |
1026-0226 1607-887X |
| publishDate |
2015-01-01 |
| description |
We study a rational planar system consisting of one linear-affine and one linear-fractional
difference equation. If all of the system’s parameters are positive (so that the positive quadrant
is invariant and the system is continuous), then we show that the unique fixed point of the
system in the positive quadrant cannot be repelling and the system does not have a snap-back
repeller. By folding the system into a second-order equation, we find special cases of the system
with some negative parameter values that do exhibit chaos in the sense of Li and Yorke within
the positive quadrant of the plane. |
| url |
http://dx.doi.org/10.1155/2015/519598 |
| work_keys_str_mv |
AT nlazaryan periodicandchaoticorbitsofadiscreterationalsystem AT hsedaghat periodicandchaoticorbitsofadiscreterationalsystem |
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1716771375254863872 |