Stochastic Stability in Fuzzy Dynamical Systems

Year 2012, Volume: 9 Issue: 1, - , 01.02.2012

Seyyed A. Ahmadi Mohammad R. Molaei

https://izlik.org/JA67LJ85HM

Abstract

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.

Keywords

Fuzzy metric space , fuzzy dynamical system , shadowing property , limit shadowing property

References

• [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.