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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

On a New Class of Rational Difference Equation zn+1 = azn+bzn−k+(α +β zn−k)/(A+Bzn−k)

Journal of Applied Nonlinear Dynamics 8(4) (2019) 569--584 | DOI:10.5890/JAND.2019.12.005

Abdul Khaliq$^{1}$, Sk. Sarif Hassan$^{2}$

$^{1}$ Mathematics Department, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore, Pakistan

$^{2}$ Department of Mathematics, Pingla Thana Mahavidyalaya, PaschimMedinipur, 721400, West Bengal, India

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Abstract

In this article, we will investigate invariant intervals, periodic character, the character of semi cycles and global asymptotic stability of all positive solutions of a nonlinear rational difference equation of order k+1, zn+1 = azn+bzn−k+(α +β zn−k)/(A+Bzn−k), n = 0,1, ..., where the parameters a, b, α,β and A, B and the initial conditions z−k, z−k+1, z−k+2, ..., z0 are arbitrary positive real numbers. We also have studied the global stability of this equation through numerically solved examples and confirm our theoretical discussion through it.

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