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Pan-American Journal of Mathematics Pan-Amer. J. Math.  |  ISSN 2832-4293 (online)  |  Open access
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Research article

Stability Chaos and Periodic Solution of Delayed Rational Recursive Sequence

Abdul Khaliq, Mubeen Alam, Sk. Sarif Hassan

Abstract

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.

How to cite

A. Khaliq, M. Alam, S. S. Hassan, Stability Chaos and Periodic Solution of Delayed Rational Recursive Sequence, Pan-Amer. J. Math. 1 (2022), 15. https://doi.org/10.28919/cpr-pajm/1-15

BibTeX
@article{Khaliq2022,
  author  = {Khaliq, Abdul and Alam, Mubeen and Hassan, Sk. Sarif},
  title   = {Stability Chaos and Periodic Solution of Delayed Rational Recursive Sequence},
  journal = {Pan-Amer. J. Math.},
  volume  = {1},
  year    = {2022},
  pages   = {15},
  doi     = {10.28919/cpr-pajm/1-15}
}