×

Chaotic maps with nonlocal coupling: Lyapunov exponents, synchronization of chaos, and characterization of chimeras. (English) Zbl 1495.37046


MSC:

37H10 Generation, random and stochastic difference and differential equations
Full Text: DOI

References:

[1] Kaneko, K.; Tsuda, I., Complex systems: chaos and beyond: a constructive approach with applications (2001), Springer: Springer Berlin · Zbl 0959.92001
[2] Lichtenberg, A. J.; Lieberman, M. A., Regular and chaotic motion (1997), Springer Verlag: Springer Verlag Berlin
[3] Kaneko, K., Physica D, 34, 1 (1989) · Zbl 0702.58043
[4] Kaneko, K., Chaos, 2, 279 (1992) · Zbl 1055.37540
[5] Mitchel, M., Complexity: a guided tour (2009), Oxford University Press: Oxford University Press Oxford · Zbl 1215.00003
[6] Acebrón, J. A.; Bonilla, L. L.; Vicente, C. J.P.; Ritort, F.; Spigler, R., Rev Mod Phys, 77, 137 (2005)
[7] Kaneko, K., Physica D, 41, 137 (1990) · Zbl 0709.58520
[8] Oushi, N. B.; Kaneko, K., Chaos, 10, 359 (2000) · Zbl 0969.37013
[9] Kuramoto, Y., Prog Theor Phys, 94, 321 (1995)
[10] Kuramoto, Y.; Nakao, H., Phys Rev Lett, 76, 4352 (1996)
[11] Kuramoto, Y.; Nakao, H., Physica D, 103, 294 (1997) · Zbl 1194.37157
[12] Viana, R. L.; Batista, A. M.; Batista, C. A.S.; de Pontes, J. C.A.; Silva, F. A.S.; Lopes, S. R., Commun Nonlinear Sci Numer Simul, 17, 2924 (2012) · Zbl 1242.93107
[13] Silva, F. A.S.; Lopes, S. R.; Viana, R. L., Commun Nonlinear Sci Numer Simul, 35, 37-52 (2016) · Zbl 1510.92030
[14] Viana, R. L.; Batista, A. M.; Batista, C. A.S.; Iarosz, K. C., Nonlinear Dyn, 87, 1589 (2017) · Zbl 1384.37044
[15] Liu, C.; Reppert, S. M., Neuron, 25, 123 (2000)
[16] Gonze, D.; Bernard, S.; Waltermann, C.; Kramer, A.; Herzel, H., Biophys J, 89, 120 (2005)
[17] Aton, S. J.; Herzog, E. D., Neuron, 48, 531 (2005)
[18] To, T. L.; Henson, M. A.; Herzog, E. D.; Doyle, F. J., Biophys J., 92, 3792 (2007)
[19] Freeman, G. M.; Webb, A. B.; Sungwen, A. N.; Herzog, E. D., Sleep Biol Rhythms, 6, 67 (2008)
[20] Kunz, H.; Achermann, P. J., J Theor Biol, 224, 63 (2003) · Zbl 1464.92018
[21] Ueda, H. R.; Hirose, K.; Iimo, M. J., J Theor Biol, 216, 501 (2002)
[22] Yamaguchi, S., Science, 302, 1408 (2003)
[23] de Haro, L.; Panda, S., J Biol Rhythms, 21, 507 (2006)
[24] Rogers, J. L.; Wille, L. T., Phys Rev E, 54, R1082 (1996)
[25] Wolfrum, M.; Omel’chenko, O. E.; Yanchuk, S.; Maistrenko, Y. L., Chaos, 21, 013112 (2011) · Zbl 1345.34067
[26] Omel’chenko, I.; Maistrenko, Y.; Hövel, P.; Schöll, E., Phys Rev Lett, 106, 234102 (2011)
[27] Omel’chenko, I.; Omel’chenko, O. E.; Hövel, P.; Schöll, E., Phys Rev Lett, 110, 224101 (2013)
[28] Abrams, D. M.; Strogatz, S. H., Int J Bifurcat Chaos, 16, 21 (2006) · Zbl 1101.37319
[29] Xie, J.; Knobloch, E.; Kao, H. C., Phys Rev E, 90, 022919 (2014)
[30] Omel’chenko, O. E., Nonlinearity, 31, R121 (2018) · Zbl 1395.34045
[31] Grosu, I.; Banerjee, R.; Roy, P. K.; Dana, S. K., Phys Rev, 80, 016212 (2009)
[32] Ghosh, D.; Grosu, I.; Dana, S. K., Chaos, 22, 033111 (2012) · Zbl 1319.93026
[33] Erratum: Phys. Rev. E 69, 045202(E) (2004)
[34] Anteneodo, C.; Batista, A. M.; Viana, R. L., Phys Lett A, 326, 227 (2004) · Zbl 1138.37338
[35] Viana, R. L.; Grebogi, C.; de S. Pinto, S. E.; Lopes, S. R.; Batista, A. M.; Kurths, J., Physica D, 206, 94 (2005) · Zbl 1099.37511
[36] Batista, C. A.S.; Viana, R. L., Physica A, 526, 120869 (2019) · Zbl 07566400
[37] Batista, A. M.; de S. Pinto, S. E.; Viana, R. L.; Lopes, S. R., Phys Rev E, 65, 056209 (2002)
[38] de S. Pinto, S. E.; Lopes, S. R.; Viana, R. L., Physica A, 303, 339 (2002) · Zbl 0979.37023
[39] Viana, R. L.; Grebogi, C.; de S. Pinto, S. E.; Lopes, S. R.; Batista, A. M.; Kurths, J., Phys Rev E, 68, 067204 (2003)
[40] Vasconcelos, D. B.; Viana, R. L.; Lopes, S. R.; Batista, A. M.; de S. Pinto, S. E., Physica A, 343, 201 (2004)
[41] de Pontes, J. C.A.; Batista, A. M.; Viana, R. L.; Lopes, S. R., Physica A, 368, 387 (2006)
[42] de Pontes, J. C.A.; Viana, R. L.; Lopes, S. R.; Batista, C. A.S.; Batista, A. M., Physica A, 387, 4417 (2008)
[43] Kuramoto, Y., Lecture notes in physics, (Araki, H., International symposium on mathematical problems in theoretical physics, vol. 39 (1975), Springer-Verlag: Springer-Verlag New York), 420
[44] Kuramoto, Y., Chemical oscillations, waves, and turbulence (1984), Springer-Verlag: Springer-Verlag New York · Zbl 0558.76051
[45] Sethia, G. C.; Sen, A., Phys Rev Lett, 112, 144101 (2014)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.