In this paper, we study the qualitative behavior of the positive solutions of a second-order rational fuzzy difference equations with initial conditions and parameters are positive fuzzy numbers. More precisely, we investigate existence of positive solutions, boundedness, persistence and stability analysis of a second-order fuzzy rational difference equation. Some numerical examples are given to verify our theoretical results.
GroveE.A. and LadasG., Periodicities in Nonlinear Difference Equations, Chapman and Hall/CRC Press, Boca Raton, 2004.
2.
SedaghatH., Nonlinear Difference Equations: Theory with Applications to Social Science Models, Springer, Netherland, 2003.
3.
DinQ., Dynamics of a discrete-Lotka-Volterra model, Advances in Difference Equations (2013), 95.
4.
DinQ. and DonchevT., Global character of a host-parasite model, Chaos, Solitons & Fractals54 (2013), 1–7.
5.
DinQ., Global stability of a population model, Chaos, Solitons & Fractals59 (2014), 119–128.
6.
DinQ., IbrahimT.F. and KhanK.A., Behavior of a competitive system of second-order difference equations, The Scientific World Journal2014 (2014), 9. Article ID 283982.
7.
DinQ. and ElsayedE.M., Stability analysis of a discrete ecological model, Computational Ecology and Software4(2) (2014), 89–103.
8.
LakshmikanthamV. and VatsalaA.S., Basic theory of fuzzy difference equations, Journal of Difference Equations & Applications8(11) (2002), 957–968.
9.
WuC. and ZhangB., Embedding problem of non-compact fuzzy number space , Fuzzy Sets & Systems1 (2000), 110, 135–142.
10.
BassaneziR.C., BarrosL.C.D. and TonelliP.A., Attractors and asymptotic stability for fuzzy dynamical systems, Fuzzy Sets & Systems113(3) (2000), 473–483.
11.
PapaschinopoulosG. and PapadopoulosB.K., On the fuzzy difference equation , Soft Computing6 (2002), 456–461.
12.
PapaschinopoulosG. and PapadopoulosB.K., On the fuzzy difference equation , Fuzzy Sets & Systems129 (2002), 73–81.
13.
PapaschinopoulosG. and StefanidouG., Boundedness and asymptotic behavior of the solutions of a fuzzy difference equation, Fuzzy Sets & Systems140 (2003), 523–539.
14.
StefanidouG. and PapaschinopoulosG., A fuzzy difference equation of rational form, Journal of Nonlinear Mathematical Physics12(2) (2005), 300–315.
15.
ZhangQ.H., YangL.H. and LiaoD.X., Behavior of solutions to a fuzzy nonlinear difference equation, Iranian Journal of Fuzzy Systems9(2) (2012), 1–12.
16.
BajoI. and LizE., Global behavior of a second-order nonlinear difference equation, Journal of Difference Equations & Applications17(10) (2011), 1471–1486.
17.
PitukM., More on Poincare’s and Perron’s theorems for difference equations, Journal of Difference Equations & Applications8 (2002), 201–216.
18.
DinQ., Asymptotic behavior of an anti-competitive system of second-order difference equations, Journal of the Egyptian Mathematical Society24 (2016), 37–43.
19.
DinQ., Stability analysis of a biological network, Network Biology4(3) (2014), 123–129.
20.
DinQ., KhanK.A. and NosheenA., Stability analysis of a system of exponential difference equations, Discrete Dynamics in Nature and Society2014 (2014), 11. Article ID 375890.
21.
DinQ., On a system of a fourth-order rational difference equations, Acta Universitatis Apulensis39 (2014), 137–150.
22.
MoyeL.A. and KapadiaA.S., Difference equation with public health applications, Marcel Dekker, Inc 270 Madison Avene New York, copyright2000, Marcel Dekker USA.
23.
UmekkenS.A., CanE. and BarakM.A., Fuzzy difference equations in finance, International Journal of Scientific and Innovative Mathematical Research2(8) (2014), 729–735.
24.
ZhanJ., Irfan AliM. and MehmoodN., On a novel uncertain soft set model: Z-soft fuzzy rough set model and corresponding decision making method, Applied Soft Computing56 (2017), 446–457.
25.
MaX., LiuQ. and ZhanJ., A survey of decision making methods based on certain hybrid soft set models, Artificial Intelligence Review47 (2017), 507–530.
26.
ZhanJ., LiuQ. and HerawanT., A novel soft rough set: Soft rough hemirings and its multicriteria group decision making, Applied Soft Computing54 (2017), 393–402.
27.
ZhanJ. and ZhuK., A novel soft rough fuzzy set: Z-soft rough fuzzy ideals of hemirings and corresponding decision making, Soft Computing21 (2017), 1923–1936.
28.
ZhanJ., LiuQ. and ZhuW., Another approach to rough soft hemirings and corresponding decision making, Soft Computing21 (2017), 3769–3780.
29.
ZadehL.A., Fuzzy sets, Information and Control8 (1965), 338–353.
