Journal of Applied Nonlinear Dynamics
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) 569584  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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