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Based on piecewise monotone interval maps and linear coupling, we study order patterns of spatiotemporal chaos. The forbidden patterns are found to arise mainly from the reduction of curve intersections due to time invariance of chaotic maps. It is proved that linear couplings may destroy the time invariance, and create the conditions for increasing intersections. We analyze the effects of chaotic map, coupling strength and coupling number order patterns. Simulation results and illustrative examples all confirm the correctness of the theoretical results.
[1] Xiang F, Qiu S S 2008 Acta Phys. Sin. 57 6138 (in Chinese)[向 菲、 丘水生 2008 57 6138]
[2] 50001
[3] Yu Z B, Feng J C 2008 Acta Phys. Sin. 57 1409 (in Chinese) [余振标、 冯久超 2008 57 1409]
[4] Chen F X, Zhang W D 2007 Chin. Phys. 16 937
[5] Long M, Qiu S S 2007 Chin. Phys. 16 2254
[6] Liu Y Z, Jiang C S, Lin C S, Jiang Y M 2007 Chin. Phys. 16 660
[7] Li F, Shu W X, Luo H L, Ren Z Z 2007 Chin. Phys. 16 650
[8] Bandt C, Pompe B 2002 Phys. Rev. Lett. 88 174102
[9] Bandt C, Keller G, Pompe B 2002 Nonlinearity 15 1595
[10] Amigóa J, Kennel M, Kocarev L 2005 Physica D 210 77
[11] Amigóa J, Kocarev L, Szczepanski J 2006 Phys. Lett. A 355 27
[12] Amigóa J, Kennel B 2008 Physica D 237 2893
[13] Bandt C 2005 Ecological Modeling 182 229
[14] Keller K, Sinn M 2005 Physica A 356 114
[15] Amigó J, Zambrano S, Sanjuán M 2007 Europhysics Lett. 79
[16] Zanin M 2008 Chaos 18 013119
[17] Hou W, Feng G L, Dong W J, Li J P 2006 Acta Phys. Sin. 55 2663 (in Chinese) [侯 威、 封国林、 董文杰、 李建平 2006 55 2663]
[18] Kuang J Y, Deng K, Huang R H 2001 Acta Phys. Sin. 50 1856 (in Chinese) [匡锦瑜、 邓 昆、 黄荣怀 2001 50 1856]
[19] Liu S B, Sun J, Xu Z Q, Liu J S 2009 Chin. Phys. B 58 6828
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[1] Xiang F, Qiu S S 2008 Acta Phys. Sin. 57 6138 (in Chinese)[向 菲、 丘水生 2008 57 6138]
[2] 50001
[3] Yu Z B, Feng J C 2008 Acta Phys. Sin. 57 1409 (in Chinese) [余振标、 冯久超 2008 57 1409]
[4] Chen F X, Zhang W D 2007 Chin. Phys. 16 937
[5] Long M, Qiu S S 2007 Chin. Phys. 16 2254
[6] Liu Y Z, Jiang C S, Lin C S, Jiang Y M 2007 Chin. Phys. 16 660
[7] Li F, Shu W X, Luo H L, Ren Z Z 2007 Chin. Phys. 16 650
[8] Bandt C, Pompe B 2002 Phys. Rev. Lett. 88 174102
[9] Bandt C, Keller G, Pompe B 2002 Nonlinearity 15 1595
[10] Amigóa J, Kennel M, Kocarev L 2005 Physica D 210 77
[11] Amigóa J, Kocarev L, Szczepanski J 2006 Phys. Lett. A 355 27
[12] Amigóa J, Kennel B 2008 Physica D 237 2893
[13] Bandt C 2005 Ecological Modeling 182 229
[14] Keller K, Sinn M 2005 Physica A 356 114
[15] Amigó J, Zambrano S, Sanjuán M 2007 Europhysics Lett. 79
[16] Zanin M 2008 Chaos 18 013119
[17] Hou W, Feng G L, Dong W J, Li J P 2006 Acta Phys. Sin. 55 2663 (in Chinese) [侯 威、 封国林、 董文杰、 李建平 2006 55 2663]
[18] Kuang J Y, Deng K, Huang R H 2001 Acta Phys. Sin. 50 1856 (in Chinese) [匡锦瑜、 邓 昆、 黄荣怀 2001 50 1856]
[19] Liu S B, Sun J, Xu Z Q, Liu J S 2009 Chin. Phys. B 58 6828
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