Chaos in nonautonomous discrete fuzzy dynamical systems
Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 2, p. 404-412.

Voir la notice de l'article provenant de la source International Scientific Research Publications

This paper is devoted to a study of relations between chaotic properties of nonautonomous dynamical system and its induced fuzzy system. More specially, we study transitivity, periodic density and sensitivity in an original nonautonomous system and its connections with the same ones in its fuzzified system.
DOI : 10.22436/jnsa.009.02.06
Classification : 37B55
Keywords: Discrete dynamical system, nonautonomous, fuzzy, chaos.

Lan, Yaoyao 1

1 Department of Mathematics and Finance, Chongqing University of Arts and Sciences, Chongqing 402160, China;Key Laboratory, Chongqing University of Arts and Sciences, Chongqing 402160, China
@article{JNSA_2016_9_2_a5,
     author = {Lan, Yaoyao},
     title = {Chaos in nonautonomous discrete fuzzy dynamical systems},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {404-412},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2016},
     doi = {10.22436/jnsa.009.02.06},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.02.06/}
}
TY  - JOUR
AU  - Lan, Yaoyao
TI  - Chaos in nonautonomous discrete fuzzy dynamical systems
JO  - Journal of nonlinear sciences and its applications
PY  - 2016
SP  - 404
EP  - 412
VL  - 9
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.02.06/
DO  - 10.22436/jnsa.009.02.06
LA  - en
ID  - JNSA_2016_9_2_a5
ER  - 
%0 Journal Article
%A Lan, Yaoyao
%T Chaos in nonautonomous discrete fuzzy dynamical systems
%J Journal of nonlinear sciences and its applications
%D 2016
%P 404-412
%V 9
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.02.06/
%R 10.22436/jnsa.009.02.06
%G en
%F JNSA_2016_9_2_a5
Lan, Yaoyao. Chaos in nonautonomous discrete fuzzy dynamical systems. Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 2, p. 404-412. doi : 10.22436/jnsa.009.02.06. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.02.06/

[1] AlSharawi, Z.; Angelosa, J.; Elaydib, S.; Rakesha, L. An extension of Sharkovsky's theorem to periodic difference equations, J. Math. Anal. Appl., Volume 316 (2006), pp. 128-141

[2] Aulbach, B.; Rasmussen, M. Approximation of attractors of nonautonomous dynamical systems, Discrete Contin. Dyn. Sys. Ser. B, Volume 5 (2005), pp. 215-238

[3] Balibrea, F.; P. Oprocha Weak mixing and chaos in nonautonomous discrete systems, Appl. Math. Lett., Volume 25 (2012), pp. 1135-1141

[4] Banks, J.; Brooks, J.; Cairns, G.; Davis, G.; Stacey, P. On Devaney's definition of chaos, Amer. Math. Monthly, Volume 99 (1992), pp. 332-334

[5] Cánovas, J. S.; Kupka, J. Topological entropy of fuzzified dynamical systems, Fuzzy Sets and Systems, Volume 165 (2011), pp. 37-49

[6] Chen, L.; Kou, H.; Luo, M. K.; Zhang, W. N. Discrete dynamical systems in L-topological space, Fuzzy Sets and Systems, Volume 156 (2005), pp. 25-42

[7] R. Devaney An introduction to chaotic dynamical systems , 2nd ed., Addison Wesley, New York, 1989

[8] Dewilde, P.; Veen, A. J. van der Time-varying Systems and Computations , Kluwer Academic Publishers, Boston, 1998

[9] Diamond, P.; Kloeden, P. E. Characterization of compact subsets of fuzzy sets, Fuzzy Sets and Systems, Volume 29 (1989), pp. 341-348

[10] Dvořáková, J. Chaos in nonautonomous discrete dynamical systems, Commun. Nonlinear Sci. Numer. Simulat., Volume 17 (2012), pp. 4649-4652

[11] Elaydi, S.; Sacker, R. Global stability of periodic orbits of nonautonomous difference equations and population biology, J. Diff. Equations, Volume 208 (2005), pp. 258-273

[12] Fedeli, A. On chaotic set-valued discrete dynamical systems, Chaos Solitons Fractals, Volume 23 (2005), pp. 1381-1384

[13] Kaleva, O. On the convergence of fuzzy sets, Fuzzy Sets and Systems, Volume 17 (1985), pp. 53-65

[14] Khan, A.; Kumar, P. Chaotic properties on time varying map and its set valued extension, Adv. Pure Math., Volume 3 (2013), pp. 359-364

[15] Khan, A.; Kumar, P. Chaotic phenomena and nonautonomous dynamical system, Global J. Theor. Appl. Math. Sci., Volume 3 (2013), pp. 31-39

[16] Kolyada, S.; L. Snoha Topological entropy of nonautonomous dynamical systems, Random Comput. Dynam., Volume 4 (1996), pp. 205-223

[17] Kupka, J. Some chaotic and mixing properties of Zadeh's Extension, IFSA/EUSFLAT Conf. (2009), pp. 589-594

[18] Kupka, J. On Devaney chaotic induced fuzzy and set-valued dynamical systems, Fuzzy Sets and Systems, Volume 117 (2011), pp. 34-44

[19] Kupka, J. On fuzzifications of discrete dynamical systems, Inform. Sci., Volume 181 (2011), pp. 2858-2872

[20] Lan, Y. Y.; Li, Q. G.; Mu, C. L.; Huang, H. Some chaotic properties of discrete fuzzy dynamical systems, Abstr. Appl. Anal., Volume 2012 (2012), pp. 1-9

[21] Li, T.; Yorke, J. Period three implies chaos, Amer. Math. Monthly, Volume 82 (1975), pp. 985-992

[22] Liu, H.; Shi, E.; Liao, G. Sensitivity of set-valued discrete systems, Nonlinear Anal., Volume 71 (2009), pp. 6122-6125

[23] Román-Flores, H.; Chalco-Cano, Y. Some chaotic properties of Zadeh's extension, Chaos Solitons Fractals, Volume 35 (2008), pp. 452-459

[24] Román-Flores, H.; Chalco-Cano, Y.; Silva, G. N.; J. Kupka On turbulent, erratic and other dynamical properties of Zadeh's extensions, Chaos, Solitons and Fractals, Volume 44 (2011), pp. 990-994

[25] Shi, Y. Chaos in nonautonomous discrete dynamical systems approached by their subsystems, RFDP of Higher Education of China, Beijing, 2012

[26] Shi, Y.; Chen, G. Chaos of time-varying discrete dynamical systems, J. Differ. Equ. Appl., Volume 15 (2009), pp. 429-449

[27] Silverman, S. On maps with dense orbits and the deffnition of chaos, Rocky. Mt. J. Math., Volume 22 (1992), pp. 353-375

[28] Tian, C.; Chen, G. Chaos of a sequence of maps in a metric space, Chaos Solitons Fractals, Volume 28 (2006), pp. 1067-1075

[29] Wang, Y. G.; Wei, G. Dynamical systems over the space of upper semicontinuous fuzzy sets, Fuzzy Sets and Systems, Volume 209 (2012), pp. 89-103

Cité par Sources :