Stability Chaos and Periodic Solution of Delayed Rational Recursive Sequence
In this paper, we will investigate a non-linear rational difference equation of higher order. Our concentration is on invariant intervals, periodic character, the character of semi cycles and global asymptotic stability of all positive solutions of sn+1=Asn+Bsn−l+(α+βsn−k)/(A0+B0sn−k), n=0,1,... wh...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Mathyze Publishers
2022-10-01
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| Series: | Pan-American Journal of Mathematics |
| Online Access: | https://mathyze.com/index.php/pajm/article/view/57 |
| Summary: | In this paper, we will investigate a non-linear rational difference equation of higher order. Our concentration is on invariant intervals, periodic character, the character of semi cycles and global asymptotic stability of all positive solutions of
sn+1=Asn+Bsn−l+(α+βsn−k)/(A0+B0sn−k), n=0,1,...
where the parameters A, B, α, β and A0, B0 and the initial conditions s−r, s−r+1, s−r+2, ..., s0 are arbitrary positive real numbers, r=max{l,k}. Finally, we study the global stability of this equation through numerically solved examples and confirm our theoretical discussion through it. |
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| ISSN: | 2832-4293 |