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Stochastic Stability in Fuzzy Dynamical Systems

Yıl 2012, Cilt: 9 Sayı: 1, - , 01.02.2012

Öz

In this paper we introduce the notion of the shadowing property for fuzzy
dynamical systems and prove that this property is invariant under fuzzy topological conjugacy.
By using of dynamical systems with the shadowing property we present a method
to construct fuzzy dynamical systems with the fuzzy shadowing property.

Kaynakça

  • [1] N. Aoki and K. Hiraide, Topological Theory of Dynamical Systems: Recent Advances, North-Holland Mathematical Library 52, North-Holland, Amsterdam 1994.
  • [2] R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Mathematics 470, Springer, Berlin 2008.
  • [3] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems 64 (1994), 395–399.
  • [4] A. George and P. Veeramani, Some theorems in fuzzy metric spaces, Journal of Fuzzy Mathematics 3 (1995), 933–940.
  • [5] A. George and P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Systems 90 (1997), 365–368.
  • [6] V. Gregori and S. Romaguera, Some properties of fuzzy metric spaces, Fuzzy Sets and Systems 115 (2000), 485–489.
  • [7] O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems 12 (1984), 215– 229.
  • [8] B. Kılı¸c and E. Ba¸s, Complex solutions for the Fisher equation and the Benjamin-BonaMahony equation, C¸ ankaya University Journal of Science and Engineering 7 (2010), 87–93.
  • [9] O. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika 11 (1975), 336–344.
  • [10] M. R. Molaei, The concept of synchronization from the observer’s viewpoint, C¸ ankaya University Journal of Science and Engineering 8 (2011), 255–262.
  • [11] S. Y. Pilyugin, Shadowing in Dynamical Systems, Lecture Notes in Mathematics 1706, Springer, Berlin 1999.
  • [12] M. Ying, A new approach for fuzzy topology (I), Fuzzy Sets and Systems 39 (1991), 303–321.
  • [13] M. Ying, A new approach for fuzzy topology (II), Fuzzy Sets and Systems 47 (1992), 221–232.
Yıl 2012, Cilt: 9 Sayı: 1, - , 01.02.2012

Öz

Kaynakça

  • [1] N. Aoki and K. Hiraide, Topological Theory of Dynamical Systems: Recent Advances, North-Holland Mathematical Library 52, North-Holland, Amsterdam 1994.
  • [2] R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Mathematics 470, Springer, Berlin 2008.
  • [3] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems 64 (1994), 395–399.
  • [4] A. George and P. Veeramani, Some theorems in fuzzy metric spaces, Journal of Fuzzy Mathematics 3 (1995), 933–940.
  • [5] A. George and P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Systems 90 (1997), 365–368.
  • [6] V. Gregori and S. Romaguera, Some properties of fuzzy metric spaces, Fuzzy Sets and Systems 115 (2000), 485–489.
  • [7] O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems 12 (1984), 215– 229.
  • [8] B. Kılı¸c and E. Ba¸s, Complex solutions for the Fisher equation and the Benjamin-BonaMahony equation, C¸ ankaya University Journal of Science and Engineering 7 (2010), 87–93.
  • [9] O. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika 11 (1975), 336–344.
  • [10] M. R. Molaei, The concept of synchronization from the observer’s viewpoint, C¸ ankaya University Journal of Science and Engineering 8 (2011), 255–262.
  • [11] S. Y. Pilyugin, Shadowing in Dynamical Systems, Lecture Notes in Mathematics 1706, Springer, Berlin 1999.
  • [12] M. Ying, A new approach for fuzzy topology (I), Fuzzy Sets and Systems 39 (1991), 303–321.
  • [13] M. Ying, A new approach for fuzzy topology (II), Fuzzy Sets and Systems 47 (1992), 221–232.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Bölüm Makaleler
Yazarlar

Seyyed A. Ahmadi Bu kişi benim

Mohammad R. Molaei Bu kişi benim

Yayımlanma Tarihi 1 Şubat 2012
Yayımlandığı Sayı Yıl 2012 Cilt: 9 Sayı: 1

Kaynak Göster

APA Ahmadi, S. A., & Molaei, M. R. (2012). Stochastic Stability in Fuzzy Dynamical Systems. Cankaya University Journal of Science and Engineering, 9(1).
AMA Ahmadi SA, Molaei MR. Stochastic Stability in Fuzzy Dynamical Systems. CUJSE. Şubat 2012;9(1).
Chicago Ahmadi, Seyyed A., ve Mohammad R. Molaei. “Stochastic Stability in Fuzzy Dynamical Systems”. Cankaya University Journal of Science and Engineering 9, sy. 1 (Şubat 2012).
EndNote Ahmadi SA, Molaei MR (01 Şubat 2012) Stochastic Stability in Fuzzy Dynamical Systems. Cankaya University Journal of Science and Engineering 9 1
IEEE S. A. Ahmadi ve M. R. Molaei, “Stochastic Stability in Fuzzy Dynamical Systems”, CUJSE, c. 9, sy. 1, 2012.
ISNAD Ahmadi, Seyyed A. - Molaei, Mohammad R. “Stochastic Stability in Fuzzy Dynamical Systems”. Cankaya University Journal of Science and Engineering 9/1 (Şubat 2012).
JAMA Ahmadi SA, Molaei MR. Stochastic Stability in Fuzzy Dynamical Systems. CUJSE. 2012;9.
MLA Ahmadi, Seyyed A. ve Mohammad R. Molaei. “Stochastic Stability in Fuzzy Dynamical Systems”. Cankaya University Journal of Science and Engineering, c. 9, sy. 1, 2012.
Vancouver Ahmadi SA, Molaei MR. Stochastic Stability in Fuzzy Dynamical Systems. CUJSE. 2012;9(1).