- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 304297, 8 pages
Chaotic Behavior of One-Dimensional Cellular Automata Rule 24
1Internet Data Center, Chongqing University of Science and Technology, Chongqing 401331, China
2School of Electrical and Information Engineering, Chongqing University of Science and Technology, Chongqing 401331, China
3Department of Mathematics and Information Engineering, Chongqing University of Education College, Chongqing 400065, China
Received 21 January 2014; Accepted 11 April 2014; Published 15 May 2014
Academic Editor: Zhen Jin
Copyright © 2014 Zujie Bie et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- J. von Neumann, The General and Logical Theory of Automata, Pergamon Press, Lendon, UK, 1951.
- H. Beigy and M. R. Meybodi, “Cellular learning automata with multiple learning automata in each cell and its applications,” IEEE Transactions on Systems, Man, and Cybernetics, Part B, vol. 40, no. 1, pp. 54–65, 2010.
- W. Pries, A. Thanailakis, and H. C. Card, “Group properties of cellular automata and VLSI applications,” IEEE Transactions on Computers, vol. C-35, no. 12, pp. 1013–1024, 1986.
- Q.-X. Liu, Z. Jin, and M.-X. Liu, “Spatial organization and evolution period of the epidemic model using cellular automata,” Physical Review E, vol. 74, no. 3, Article ID 031110, 6 pages, 2006.
- G.-Q. Sun, Z. Jin, and L. Li, “Emergent turing pattern in epidemic spreading using cellular automaton,” International Journal of Modern Physics B, vol. 25, no. 32, pp. 4605–4613, 2011.
- G.-Q. Sun, Z. Jin, L.-P. Song, A. Chakraborty, and B.-L. Li, “Phase transition in spatial epidemics using cellular automata with noise,” Ecological Research, vol. 26, no. 2, pp. 333–340, 2011.
- S. Nandi, B. K. Kar, and P. Pal Chaudhuri, “Theory and applications of cellular automata in cryptography,” IEEE Transactions on Computers, vol. 43, no. 12, pp. 1346–1357, 1994.
- A. Abdo, S. Lian, I. Ismail, M. Amin, and H. Diab, “A cryptosystem based on elementary cellular automata,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 1, pp. 136–147, 2013.
- J.-C. Jeon and K.-Y. Yoo, “Elliptic curve based hardware architecture using cellular automata,” Mathematics and Computers in Simulation, vol. 79, no. 4, pp. 1197–1203, 2008.
- Z. Eslami, S. H. Razzaghi, and J. Z. Ahmadabadi, “Secret image sharing based on cellular automata and steganography,” Pattern Recognition, vol. 43, no. 1, pp. 397–404, 2010.
- R.-J. Chen and S.-J. Horng, “Novel SCAN-CA-based image security system using SCAN and 2-D von Neumann cellular automata,” Signal Processing: Image Communication, vol. 25, no. 6, pp. 413–426, 2010.
- L. Feng, X. Liao, Q. Han, and L. Song, “Modeling and analysis of peer-to-peer botnets,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 865075, 18 pages, 2012.
- L. Feng, X. Liao, Q. Han, and H. Li, “Dynamical analysis and control strategies on malware propagation model,” Applied Mathematical Modelling, vol. 37, no. 16-17, pp. 8225–8236, 2013.
- L.-P. Song, Z. Jin, G.-Q. Sun, J. Zhang, and X. Han, “Influence of removable devices on computer worms: dynamic analysis and control strategies,” Computers & Mathematics with Applications, vol. 61, no. 7, pp. 1823–1829, 2011.
- W. M. Van Ballegooijen and M. C. Boerlijst, “Emergent trade-offs and selection for outbreak frequency in spatial epidemics,” Proceedings of the National Academy of Sciences of the United States of America, vol. 101, no. 52, pp. 18246–18250, 2004.
- G.-Q. Sun, Q.-X. Liu, Z. Jin, A. Chakraborty, and B.-L. Li, “Influence of infection rate and migration on extinction of disease in spatial epidemics,” Journal of Theoretical Biology, vol. 264, no. 1, pp. 95–103, 2010.
- Q. Han, C. D. Li, and J. J. Huang, “Anticipating synchronization of chaotic systems with time delay and parameter mismatch,” Chaos, vol. 19, Article ID 013104, 10 pages, 2009.
- Q. Han, C. Li, and T. Huang, “Anticipating synchronization of a class of chaotic systems,” Chaos, vol. 19, no. 2, Article ID 023105, 10 pages, 2009.
- F. Bao, “Cryptanalysis of a partially known cellular automata cryptosystem,” IEEE Transactions on Computers, vol. 53, no. 11, pp. 1493–1497, 2004.
- M. Tomassini and M. Perrenoud, “Cryptography with cellular automata,” Applied Soft Computing, vol. 1, no. 2, pp. 151–160, 2001.
- S. Wolfram, “Universality and complexity in cellular automata,” Physica D, vol. 10, no. 1-2, pp. 1–35, 1984.
- S. Wolfram, Theory and Applications of Cellular Automata, vol. 1 of Advanced Series on Complex Systems, World Scientific Publishing, Singapore, 1986.
- S. Wolfram, A New Kind of Science, Wolfram Media, Champaign, Ill, USA, 2002.
- F.-Y. Chen, W.-F. Jin, G.-R. Chen, F.-F. Chen, and L. Chen, “Chaos of elementary cellular automata rule 42 of Wolfram's class II,” Chaos, vol. 19, no. 1, Article ID 013140, 6 pages, 2009.
- F.-F. Chen and F.-Y. Chen, “Complex dynamics of cellular automata rule 119,” Physica A, vol. 388, no. 6, pp. 984–990, 2009.
- L. Chen, F. Y. Chen, F. Chen, and W. Jin, “Complex symbolic dynamics of bernoulli shift cellular automata rule,” in Proceedings of the 9th International Conference for Young Computer Scientists (ICYCS '08), pp. 2868–2873, November 2008.
- Q. Han, X. Liao, C. Li, and L. Feng, “Complex dynamics behaviors in cellular automata rule 35,” Journal of Cellular Automata, vol. 6, no. 6, pp. 487–504, 2011.
- Q. Han, X. Liao, and C. Li, “Complex dynamic behaviors in cellular automata rule 14,” Discrete Dynamics in Nature and Society, Article ID 258309, 12 pages, 2012.
- L. O. Chua, V. I. Sbitnev, and S. Yoon, “A nonlinear dynamics perspective of Wolfram's new kind of science. III. Predicting the unpredictable,” International Journal of Bifurcation and Chaos, vol. 14, no. 11, pp. 3689–3820, 2004.
- L. O. Chua, V. I. Sbitnev, and S. Yoon, “A nonlinear dynamics perspective of Wolfram's new kind of science. IV. From Bernoulli shift to spectrum,” International Journal of Bifurcation and Chaos, vol. 15, no. 4, pp. 1045–1183, 2005.
- J. Guan, S. Shen, C. Tang, and F. Chen, “Extending Chua's global equivalence theorem on Wolfram's new kind of science,” International Journal of Bifurcation and Chaos, vol. 17, no. 12, pp. 4245–4259, 2007.
- B. P. Kitchens, Symbolic Dynamics: One-Sided, Two-Sided and Countable State Markov Shifts, Universitext, Springer, Berlin, Germany, 1998.
- Z. Zhou, Symbolic Dynamics, Shanghai Scientific and Technological Education Publishing House, Shanghai, China, 1997, (Chinese).
- L. P. Shilnikov, A. L. Shilnikov, D. V. Turaev, and L. O. Chua, Methods of Qualitative Theory in Nonlinear Dynamics. Part I, vol. 4 of World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, World Scientific Publishing, River Edge, NJ, USA, 1998.
- T. Y. Li and J. A. Yorke, “Period three implies chaos,” The American Mathematical Monthly, vol. 82, no. 10, pp. 985–992, 1975.