Solutions to conjectures on a nonlinear recursive equation

Öcalan, Özkan, and Duman, Oktay. "Solutions to conjectures on a nonlinear recursive equation." Czechoslovak Mathematical Journal 70.3 (2020): 867-880. <http://eudml.org/doc/297201>.

@article{Öcalan2020,
abstract = {We obtain solutions to some conjectures about the nonlinear difference equation \[ x\_\{n+1\}=\alpha +\beta x\_\{n-1\} \{\rm e\}^\{-x\_\{n\}\}, \quad n=0,1,\cdots , \ \alpha ,\beta >0. \] More precisely, we get not only a condition under which the equilibrium point of the above equation is globally asymptotically stable but also a condition under which the above equation has a unique positive cycle of prime period two. We also prove some further results.},
author = {Öcalan, Özkan, Duman, Oktay},
journal = {Czechoslovak Mathematical Journal},
keywords = {recursive equation; nonlinear difference equation; equilibrium point; stability},
language = {eng},
number = {3},
pages = {867-880},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Solutions to conjectures on a nonlinear recursive equation},
url = {http://eudml.org/doc/297201},
volume = {70},
year = {2020},
}

TY - JOUR
AU - Öcalan, Özkan
AU - Duman, Oktay
TI - Solutions to conjectures on a nonlinear recursive equation
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 3
SP - 867
EP - 880
AB - We obtain solutions to some conjectures about the nonlinear difference equation \[ x_{n+1}=\alpha +\beta x_{n-1} {\rm e}^{-x_{n}}, \quad n=0,1,\cdots , \ \alpha ,\beta >0. \] More precisely, we get not only a condition under which the equilibrium point of the above equation is globally asymptotically stable but also a condition under which the above equation has a unique positive cycle of prime period two. We also prove some further results.
LA - eng
KW - recursive equation; nonlinear difference equation; equilibrium point; stability
UR - http://eudml.org/doc/297201
ER -