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 |
| _version_ | 1797388593709187072 |
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| author | Abdul Khaliq Mubeen Alam Sk. Sarif Hassan |
| author_facet | Abdul Khaliq Mubeen Alam Sk. Sarif Hassan |
| author_sort | Abdul Khaliq |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-08T22:43:01Z |
| format | Article |
| id | doaj.art-1cdfd219422e47649d59ed32e900a12f |
| institution | Directory Open Access Journal |
| issn | 2832-4293 |
| language | English |
| last_indexed | 2024-03-08T22:43:01Z |
| publishDate | 2022-10-01 |
| publisher | Mathyze Publishers |
| record_format | Article |
| series | Pan-American Journal of Mathematics |
| spelling | doaj.art-1cdfd219422e47649d59ed32e900a12f2023-12-17T09:16:13ZengMathyze PublishersPan-American Journal of Mathematics2832-42932022-10-011010.28919/cpr-pajm/1-1515Stability Chaos and Periodic Solution of Delayed Rational Recursive SequenceAbdul KhaliqMubeen AlamSk. Sarif HassanIn 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.https://mathyze.com/index.php/pajm/article/view/57 |
| spellingShingle | Abdul Khaliq Mubeen Alam Sk. Sarif Hassan Stability Chaos and Periodic Solution of Delayed Rational Recursive Sequence Pan-American Journal of Mathematics |
| title | Stability Chaos and Periodic Solution of Delayed Rational Recursive Sequence |
| title_full | Stability Chaos and Periodic Solution of Delayed Rational Recursive Sequence |
| title_fullStr | Stability Chaos and Periodic Solution of Delayed Rational Recursive Sequence |
| title_full_unstemmed | Stability Chaos and Periodic Solution of Delayed Rational Recursive Sequence |
| title_short | Stability Chaos and Periodic Solution of Delayed Rational Recursive Sequence |
| title_sort | stability chaos and periodic solution of delayed rational recursive sequence |
| url | https://mathyze.com/index.php/pajm/article/view/57 |
| work_keys_str_mv | AT abdulkhaliq stabilitychaosandperiodicsolutionofdelayedrationalrecursivesequence AT mubeenalam stabilitychaosandperiodicsolutionofdelayedrationalrecursivesequence AT sksarifhassan stabilitychaosandperiodicsolutionofdelayedrationalrecursivesequence |