Sensitive dependence on initial conditions for cellular automata

Chaos

Volumn 7, Issue 4, 1997, Pages 688-693

  Urías, Jesús ^a   Rechtman, Raúl ^b   Enciso, Agustín ^c  

^a UNIVERSIDAD AUTÓNOMA DE SAN LUIS POTOSÍ   (Mexico)

^b INSTITUTO DE CIENCIAS FÍSICAS   (Mexico)

^c UNIVERSIDAD AUTÓNOMA DE ZACATECAS   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040562586     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.166266     Document Type: Article

References (19)

1. R. L. Devaney, An Introduction to Chaotic Systems (Addison-Wesley, Reading, MA, 1989).
2. J. Banks, J. Brooks, G. Cairns, G. Davis, and P. Stacy, "On Devaney's definition of chaos," Math. Mon. 99, 332 (1992).
3. E. Glasner and B. Weiss, "Sensitive dependence on initial conditions," Nonlinearity 6, 1067 (1993).
4. J. Guckenheimer, "Sensitive dependence on initial conditions for one dimensional maps," Commun. Math. Phys. 70, 113 (1979).
5. S. Wolfram, "Universality and complexity in cellular automata," Physica D 10, 1 (1984).
6. F. Bagnoli, R. Rechtman, and S. Ruffo, "Damage spreading and Lyapunov exponents in cellular automata," Phys. Lett. A 172, 34 (1992).
7. G. Y. Vichniac, "Boolean derivatives on cellular automata," Physica D 43, 63 (1990).
8. F. Bagnoli, "Boolean derivatives and computation of cellular automata," Int. J. Mod. Phys. C 3, 307 (1992).
9. M. A. Shereshevsky. "Lyapunov exponents for one dimensional cellular automata," J. Nonlinear Sci. 2, 1 (1992).
10. D. A. Lind, "Applications of ergodic theory and sofic systems to cellular automata," Physica D 10, 36 (1984).
11. M. Denker, C. Grillenberger, and K. Sigmund, Ergodic Theory on Compact Spaces, Springer Lecture Notes in Mathematics, No. 527 (Springer-Verlag, Berlin, 1976).
12. I. M. Vinogradov, Elements of Number Theory (Dover, New York, 1954).
13. J. Urías, G. Salazar-Anaya, E. Ugalde, and A. Enciso, "Traveling patterns in cellular automata," Chaos 6, 493 (1996).
14. P. Grassberger, "Table 6: Statistical properties," in Cellular Automata and Complexity, edited by S. Wolfram (Addison-Wesley, New York, 1994), pp. 542-543.
15. J. Kari, "Rice's theorem for the limit sets of cellular automata," Theor. Comput. Sci. 127, 229 (1994).
16. L. Hurd, J. Kari, and K. Culik, "The topological entropy of cellular automata is uncomputable," Ergodic Theory of Dynamical Systems 12, 255 (1992).
17. S. Ponce Dawson, "Strange nonattracting chaotic sets, crises, and fluctuating Lyapunov exponents," Phys. Rev. Lett. 76, 4348 (1996).
18. J. P. Crutchfield and J. E. Hanson, "Turbulent pattern bases for cellular automata," Physica D 69, 279 (1993).
19. H. A. Gutowitz, J. D. Victor, and B. W. Knight, "Local structure theory for cellular automata," 28, 18 (1987).