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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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 |
| Summary: | 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. |
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| ISSN: | 1026-0226 1607-887X |