This paper is mainly concerned with a kind of coupled map lattices (CMLs). New definitions of dense δ-chaos and dense chaos (which is a special case of dense δ-chaos with δ = 0) in discrete spatiotemporal systems are given and sufficient conditions for these systems to be densely chaotic or densely δ-chaotic are derived.
<p>[1] T. Li and J. Yorke, “Period 3 implies chaos”, Amer. math. Monthly,
Vol. 82 No. 10, pp. 985-992, 1975.
[2] R. L. Devaney, “An introduction to chaotic dynamical”, Addison Wesley,
1989.
[3] J. Banks, etal., “On Devaney’s definition of chaos”, Amer. math. Monthly,
Vol. 99 No. 4, pp. 332-334, 1992.
[4] L. Snoha, “Dense chaos”, Math. Univ. Carolin. Vol. 33 No. 4, pp. 747-
752, 1992.
[5] S. Ruette, “Dense chaos for continuous interval maps”, Nonlinearity,
Vol. 18, No. 4, pp. 1691-1698, 2005.
[6] K. Kaneko, editor, “Theory and application of coupled map lattices”.
(John Wiley and Sons, 1993).
[7] K. Kaneko, “Towards thermodynamics of spatiotemporal chaos”, Prog.
Theor. Phys. Suppl., Vol. 263 No. 99, pp. 263-287, 1989.
[8] H. Shibata , “KS entropy and mean Lyapunov exponent for coupled map
lattices”, Physica A., Vol. 292 No. 1, pp. 182-192, 2001.
[9] HP. Lu , SH. Wang , XW. Li, et al., “A new spatiotemporally chaotic
cryptosystem and its security and performance analyses”, Chaos, Vol. 14
No. 3, pp. 617-629, 2004.
[10] G. Hu and Z. Qu, “Controlling spatiotemporal chaos in coupled map
lattice systems”, Phys. Rev. Lett., Vol. 72 No. 1, pp. 68-71, 1994.
[11] G. Hu, J. Xian, etal., “Synchronization of spatiotemporal chaos and
its applications”, phys. Rev. E., Vol. 56 No. 8, pp. 2738-2746, 1997.
[12] F. Willeboordse, “The spatial logistic map as a simple prototype for
spatiotemporal chaos”, Chaos, Vol. 13 No. 2, pp. 533-540, 2003.
[13] G. Chen and S. Liu, “On generalized synchronization of spatial chaos”,
Chaos, Solitons and Fractals, Vol. 15 No. 2, pp. 311-318, 2003.
[14] G. Chen, C. Tian, and Y. Shi, “Stability and chaos in 2-D discrete
systems”, Chaos, Solitons and Fractals, Vol. 25 No. 3, pp. 637-647, 2005.
[15] C. Tian and G. Chen, “Chaos in the sence of Li-Yorke in coupled map
lattices”, Physica A, Vol. 376 No. 8, pp. 246-252, 2007.</p>
<p>[1] T. Li and J. Yorke, “Period 3 implies chaos”, Amer. math. Monthly,
Vol. 82 No. 10, pp. 985-992, 1975.
[2] R. L. Devaney, “An introduction to chaotic dynamical”, Addison Wesley,
1989.
[3] J. Banks, etal., “On Devaney’s definition of chaos”, Amer. math. Monthly,
Vol. 99 No. 4, pp. 332-334, 1992.
[4] L. Snoha, “Dense chaos”, Math. Univ. Carolin. Vol. 33 No. 4, pp. 747-
752, 1992.
[5] S. Ruette, “Dense chaos for continuous interval maps”, Nonlinearity,
Vol. 18, No. 4, pp. 1691-1698, 2005.
[6] K. Kaneko, editor, “Theory and application of coupled map lattices”.
(John Wiley and Sons, 1993).
[7] K. Kaneko, “Towards thermodynamics of spatiotemporal chaos”, Prog.
Theor. Phys. Suppl., Vol. 263 No. 99, pp. 263-287, 1989.
[8] H. Shibata , “KS entropy and mean Lyapunov exponent for coupled map
lattices”, Physica A., Vol. 292 No. 1, pp. 182-192, 2001.
[9] HP. Lu , SH. Wang , XW. Li, et al., “A new spatiotemporally chaotic
cryptosystem and its security and performance analyses”, Chaos, Vol. 14
No. 3, pp. 617-629, 2004.
[10] G. Hu and Z. Qu, “Controlling spatiotemporal chaos in coupled map
lattice systems”, Phys. Rev. Lett., Vol. 72 No. 1, pp. 68-71, 1994.
[11] G. Hu, J. Xian, etal., “Synchronization of spatiotemporal chaos and
its applications”, phys. Rev. E., Vol. 56 No. 8, pp. 2738-2746, 1997.
[12] F. Willeboordse, “The spatial logistic map as a simple prototype for
spatiotemporal chaos”, Chaos, Vol. 13 No. 2, pp. 533-540, 2003.
[13] G. Chen and S. Liu, “On generalized synchronization of spatial chaos”,
Chaos, Solitons and Fractals, Vol. 15 No. 2, pp. 311-318, 2003.
[14] G. Chen, C. Tian, and Y. Shi, “Stability and chaos in 2-D discrete
systems”, Chaos, Solitons and Fractals, Vol. 25 No. 3, pp. 637-647, 2005.
[15] C. Tian and G. Chen, “Chaos in the sence of Li-Yorke in coupled map
lattices”, Physica A, Vol. 376 No. 8, pp. 246-252, 2007.</p>
@article{"International Journal of Engineering, Mathematical and Physical Sciences:65369", author = "Tianxiu Lu and Peiyong Zhu", title = "Dense Chaos in Coupled Map Lattices", abstract = "This paper is mainly concerned with a kind of coupled map lattices (CMLs). New definitions of dense δ-chaos and dense chaos (which is a special case of dense δ-chaos with δ = 0) in discrete spatiotemporal systems are given and sufficient conditions for these systems to be densely chaotic or densely δ-chaotic are derived.
", keywords = "Discrete spatiotemporal systems, coupled map lattices,
dense δ-chaos, Li-Yorke pairs.", volume = "7", number = "4", pages = "711-4", }
