Transitivity and Chaoticity in 1-D Cellular Automata - International Journal of Modern Nonlinear Theory and Application

IJMNTA > Vol.2 No.1, March 2013

International Journal of Modern Nonlinear Theory and Application

Volume 2, Issue 1 (March 2013)

ISSN Print: 2167-9479 ISSN Online: 2167-9487

Google-based Impact Factor: 0.27 Citations

Transitivity and Chaoticity in 1-D Cellular Automata ()

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Download as PDF (Size: 110KB) PP. 69-73

DOI: 10.4236/ijmnta.2013.21A008 3,395 Downloads 6,783 Views Citations

Author(s)

Fangyue Chen, Guanrong Chen, Weifeng Jin

Affiliation(s)

College of Pharmaceutical Sciences, Zhejiang Chinese Medical University, Hangzhou, China.
Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China.
School of Science, Hangzhou Dianzi University, Hangzhou, China.

ABSTRACT

Recent progress in symbolic dynamics of cellular automata (CA) shows that many CA exhibit rich and complicated Bernoulli-shift properties, such as positive topological entropy, topological transitivity and even mixing. Noticeably, some CA are only transitive, but not mixing on their subsystems. Yet, for one-dimensional CA, this paper proves that not only the shift transitivity guarantees the CA transitivity but also the CA with transitive non-trivial Bernoulli subshift of finite type have dense periodic points. It is concluded that, for one-dimensional CA, the transitivity implies chaos in the sense of Devaney on the non-trivial Bernoulli subshift of finite types.

KEYWORDS

Bernoulli Subshift of Finite Type; Cellular Automata; Devaney Chaos; Symbolic Dynamics; Topological Transitivity

Share and Cite:

F. Chen, G. Chen and W. Jin, "Transitivity and Chaoticity in 1-D Cellular Automata," International Journal of Modern Nonlinear Theory and Application, Vol. 2 No. 1A, 2013, pp. 69-73. doi: 10.4236/ijmnta.2013.21A008.

Cited by

[1]	Infinite Number of Disjoint Chaotic Subsystems of Cellular Automaton Rule 106
	Applied Mathematics, 2014

[2]	From Glider to Chaos: A Transitive Subsystem Derived From Glider B of CA Rule 110
	P Liu, F Chen, L Si, F Wang - worldcomp-proceedings.com, 2013

[3]	Chaotic Subsystem Come From Glider E 3 of CA Rule 110
	L Si, F Chen, F Wang, P Liu - world-comp.org, 2013

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