BEHAVIOR OF SOLUTIONS TO A FUZZY NONLINEAR DIFFERENCE EQUATION

Document Type: Research Paper

Authors

1 Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang, Guizhou 550004, P. R. China

2 Department of Mathematics, Hunan City University, Yiyang, Hunan 413000, P. R. China

3 Basic Science Department, Hunan Institute of Technology, Hengyang, Hunan 421002, P. R. China

Abstract

In this paper, we study the existence, asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equation
$$ x_{n+1}=frac{Ax_n+x_{n-1}}{B+x_{n-1}}, n=0,1,cdots,$$
 where $(x_n)$ is a sequence of positive fuzzy number, $A, B$ are positive fuzzy numbers and the initial conditions $x_{-1}, x_0$ are positive fuzzy numbers.

Keywords


bibitem{AbAl: Mfs}
  S. Abbasbandy and M. Alavi, {it A method for solving fuzzy linear system}, Iranian Journal of Fuzzy Systems, {bf 2} (2005), 37-43.

bibitem{BeFr: Aam}
  D. Benest and C. Froeschle, {it Analysis and modelling of discrete dynamical
  systems}, Gordon and Breach Science Publishers, The Netherland, 1998.

  bibitem{DeKo: Abf}
  E. Y. Deeba and A. De Korvin, {it Analysis of fuzzy difference equations of
  a model of $CO_2$ level in the blood}, Appl. Math. Lett., {bf 12} (1999), 33-40.

 bibitem{DeKo:Afd}
 E. Y. Deeba, A. De Korvin and E. L. Koh, {it A fuzzy difference equation with an
 application}, J. Difference Equation Appl., {bf 2} (1996), 365-374.

 bibitem{DeLa: Nsc}
  R. DeVault, G. Ladas and S. W. Schultz, {it Necessary and sufficient conditions
  the boundedness of $x_{n+1}=A/x_n^p+B/x_{n-1}^q$}, J. Difference
  Equations Appl., {bf 3} (1998), 259-266.


 bibitem{DeLa: Ors}
  R. DeVault, G. Ladas and S. W. Schultz, {it On the recursive sequence $x_{n+1}=A/x_n+1/x_{n-2}$}, Proc. Amer. Math. Soc.,
  {bf 126} (1998), 3257-3261.

bibitem{KoLa:Gbn}
 V. L. Kocic and G. Ladas, {it Golobal behavior of nonlinear difference
 equations of higher order with applications}, Kluwer Academic Publishers, 1993.


bibitem{KuLa: Rde}
 M. R. S. Kulenvic, G. Ladas and N. R. Prokup, {it A rational difference equation}, Comput. Math. Appl., {bf 41} (2001),
 671-678.


 bibitem{LiSu: Drd}
 W. Li and H. Sun, {it Dynamics of a rational difference equation}, Appl. Math. Comput.,
 {bf 163} (2005), 577-591.

 bibitem{PaPa: Ofd1}
 G. Papaschinopoulos and B. K. Papadopoulos, {it On the fuzzy difference equation $x_{n+1}=A+B/x_n$},
  Soft Comput., {bf 6} (2002), 456-461.

bibitem{PaPa:Ofd2}
 G. Papaschinopoulos and B. K. Papadopoulos, {it On the fuzzy difference equation
 $x_{n+1}=A+x_n/x_{n-m}$}, Fuzzy Sets and Systems, {bf 129} (2002), 73-81.

bibitem{PaSc: Ost}
  G. Papaschinopoulos and C. J. Schinas, {it On a systems of two nonlinear difference equation},
  J. Math. Anal. Appl., {bf 219} (1998), 415-426.

bibitem{PaSc: Ofd}
  G. Papaschinopoulos and C. J. Schinas, {it On the fuzzy difference equation $x_{n+1}=sum_{i=0}^{k-1}A_i/x_{n-i}^{p_i}+1/x_{n-k}^{p_k}$},
  J. Difference Equation Appl., {bf 6(7)} (2000), 85-89.

 bibitem{PaSt: Bab}
G. Papaschinopoulos and G. Stefanidou, {it Boundedness and asymptotic
behavior of the solutions of a fuzzy difference equation}, Fuzzy Sets and Systems, {bf 140} (2003), 523-539.

  bibitem{PhPu: Gai}
  C. G. Philos, I. K. Purnaras and Y. G. Sficas, {it Global attractivity in a
  nonlinear difference equation}, Appl. Math. Comput., {bf 62} (1994), 249-258.

bibitem{StPa: Fde}
 G. Stefanidou and G. Papaschinopoulos, {it A fuzzy difference equation of a rational form}, J. Nonlin. Math. Phys.,
 Supplement, {bf 12(2)} (2005), 300-315.

 

bibitem{WuZh: Epn}
  C. Wu and B. Zhang, {it Embedding problem of noncompact fuzzy number space
  $E^{sim}$}, Fuzzy Sets and Systems, {bf 105} (1999), 165-169.