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The chimera states and cluster chimera states in a globally coupled both discontinuous-and-non-invertible-map lattices are studied using the order parameters and spatial-time-amplitude patterns. The result show that chimera states and cluster chimera states are sensitive depends on the choice of the coupling strength, and they are induced by the interaction between the discontinuity and the non-invertibility in coupled system. We also discuss the conditions for the chimera states existing in this system.
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Keywords:
- discontinuous map /
- chimera state /
- cluster states
[1] Kuramoto Y, Battogtokh D 2002 Non. Phen. Complex. Syst. 5 380
[2] Rattenborg N C, Amlarlcr C J, Lima S L 2000 Neurosci. Biobehav. R 24 817
[3] Mathews C G, Lesku J A, Lima S L, Amlaner C J 2006 Ethology 112 286
[4] Dwight B, Laurette S, Tuckerman 2005 Phys. Rev. Lett. 94 014502
[5] Abrams D M, Strogatz S H 2006 Int. J. Bifurc. Chaos 16 21
[6] Abrams D M, Mirollo R, Strogatz S H, Wiley D A 2008 Phys. Rev. Lett. 101 084103
[7] Sethia G C, Sen A, Atay F M 2008 Phys. Rev. Lett. 100 144102
[8] Omel'chenko O E, Maistrenko Y L, Tass P A 2008 Phys. Rev. Lett. 100 044105
[9] Laing C R 2010 Phys. Rev. E 81 066221
[10] Wolfrum M, Omel'chenko O 2011 Phys. Rev. E 84 015201
[11] Omel'chenko I, Maistrenko Y, Hovel P, Schull E 2011 Phys. Rev. Lett. 106 234102
[12] Beta C, Moula M G, Mikhailov A S, Rotermund H H, Ertl G 2004 Phys. Rev. Lett. 93 188302
[13] Alexander S M, Kenneth S 2006 Phys. Rep. 425 79
[14] Simbarashe N, Mark R T, Kenneth S 2013 Phys. Rev. Lett. 110 244102
[15] Swindale N V 1980 Proc. R. Soc. Lond. B 208 243
[16] Bard E, John C, George O 1986 The Veliger 28 369
[17] Murray J D, Myerscough M R 1991 J. Theor. Biol. 149 339
[18] Sangeeta R U, Ramakrishna R 2013 Phys. Rev. E 88 032902
[19] Mark R T, Simbarashe N, Kenneth S 2012 Nat. Phys. 10 1038
[20] Aaron M H, Thomas E M, Rajarshi R, Philipp H, Iryna O, Eckehard S 2012 Nat. Phys. 10 1038 )
[21] Zhu Y, Zheng Z G, Yang J Z 2014 Phys. Rev. E 89 022914
[22] Martens E A, Laing C R 2010 Phys. Rev. Lett. 104 044101
[23] Chad G, Ghislain S Y, Jorn D 2013 Phys. Rev. Lett. 111 134101
[24] Grudzinski K, Zebrowski J J 2004 Physica A 336 153
[25] Ren H P, Liu D 2005 Chin. Phys. 14 1352
[26] He D R, Wang B H, Bauer M, Habip S, Krueger U, Martienssen W, Christiansen B 1994 Physica D 79 335
[27] He D R, Bauer M, Habip S, Krueger U, Martienssen W, Christiansen B, Wang B H 1992 Phys. Lett. A 171 61
[28] Qu S X, Wu S G, He D R 1997 Phys. Lett. A 231 152
[29] Qu S X, Wu S G, He D R 1998 Phys. Rev. E 57 402
[30] Tan H F, Jin T, Qu S X 2012 Acta Phys. Sin. 61 040507 (in Chinese) [谭红芳, 金涛, 屈世显 2012 61 040507]
[31] Qu S X, Lu Y Z, Zhang L, He D R 2008 Chin. Phys. B 17 4418
[32] Santos A M, Viann R L, Lopes S R 2002 Phys. Rev. E 65 056209
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[1] Kuramoto Y, Battogtokh D 2002 Non. Phen. Complex. Syst. 5 380
[2] Rattenborg N C, Amlarlcr C J, Lima S L 2000 Neurosci. Biobehav. R 24 817
[3] Mathews C G, Lesku J A, Lima S L, Amlaner C J 2006 Ethology 112 286
[4] Dwight B, Laurette S, Tuckerman 2005 Phys. Rev. Lett. 94 014502
[5] Abrams D M, Strogatz S H 2006 Int. J. Bifurc. Chaos 16 21
[6] Abrams D M, Mirollo R, Strogatz S H, Wiley D A 2008 Phys. Rev. Lett. 101 084103
[7] Sethia G C, Sen A, Atay F M 2008 Phys. Rev. Lett. 100 144102
[8] Omel'chenko O E, Maistrenko Y L, Tass P A 2008 Phys. Rev. Lett. 100 044105
[9] Laing C R 2010 Phys. Rev. E 81 066221
[10] Wolfrum M, Omel'chenko O 2011 Phys. Rev. E 84 015201
[11] Omel'chenko I, Maistrenko Y, Hovel P, Schull E 2011 Phys. Rev. Lett. 106 234102
[12] Beta C, Moula M G, Mikhailov A S, Rotermund H H, Ertl G 2004 Phys. Rev. Lett. 93 188302
[13] Alexander S M, Kenneth S 2006 Phys. Rep. 425 79
[14] Simbarashe N, Mark R T, Kenneth S 2013 Phys. Rev. Lett. 110 244102
[15] Swindale N V 1980 Proc. R. Soc. Lond. B 208 243
[16] Bard E, John C, George O 1986 The Veliger 28 369
[17] Murray J D, Myerscough M R 1991 J. Theor. Biol. 149 339
[18] Sangeeta R U, Ramakrishna R 2013 Phys. Rev. E 88 032902
[19] Mark R T, Simbarashe N, Kenneth S 2012 Nat. Phys. 10 1038
[20] Aaron M H, Thomas E M, Rajarshi R, Philipp H, Iryna O, Eckehard S 2012 Nat. Phys. 10 1038 )
[21] Zhu Y, Zheng Z G, Yang J Z 2014 Phys. Rev. E 89 022914
[22] Martens E A, Laing C R 2010 Phys. Rev. Lett. 104 044101
[23] Chad G, Ghislain S Y, Jorn D 2013 Phys. Rev. Lett. 111 134101
[24] Grudzinski K, Zebrowski J J 2004 Physica A 336 153
[25] Ren H P, Liu D 2005 Chin. Phys. 14 1352
[26] He D R, Wang B H, Bauer M, Habip S, Krueger U, Martienssen W, Christiansen B 1994 Physica D 79 335
[27] He D R, Bauer M, Habip S, Krueger U, Martienssen W, Christiansen B, Wang B H 1992 Phys. Lett. A 171 61
[28] Qu S X, Wu S G, He D R 1997 Phys. Lett. A 231 152
[29] Qu S X, Wu S G, He D R 1998 Phys. Rev. E 57 402
[30] Tan H F, Jin T, Qu S X 2012 Acta Phys. Sin. 61 040507 (in Chinese) [谭红芳, 金涛, 屈世显 2012 61 040507]
[31] Qu S X, Lu Y Z, Zhang L, He D R 2008 Chin. Phys. B 17 4418
[32] Santos A M, Viann R L, Lopes S R 2002 Phys. Rev. E 65 056209
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