Abstract
A network is defined as a collection of points (called nodes or vertices) joined together in pairs by lines called edges. Many systems in physics, engineering, biology and social sciences can be thought of as networks. An array of coupled systems can be considered as a network where the nodes represent the elements or units of the system and the edges represent the interactions or couplings between them. Networks of coupled systems are used to model biological oscillator networks [1–5], excitable media [6], neural networks [7–10] and genetic networks [11–13]. A network composed of a number of interacting systems (identical or nonidentical) often forms a complex dynamical system with new fascinating properties that are not realizable in the individual systems. The fascinating properties include synchronous oscillations, induced oscillations, fast system response, computational power and so on.
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References
A.T. Winfree, The Geometry of Biological Time (Springer, New York, 1980)
Y. Kuramoto, Chemical Oscillations, Waves and Turbulence (Springer, Berlin, 1984)
S.H. Strogatz, I. Stewart, Sci. Am. 269, 102 (1993)
P.C. Bressloff, S. Coombes, B. De Souza, Phys. Rev. Lett. 79, 2791 (1997)
M.E.J. Newman, Networks: An Introduction (Oxford University Press, Oxford, 2010)
M. Gerhardt, H. Schuster, J.J. Tysor, Science 247, 1563 (1990)
G. Joya, M.A. Atencia, F. Sandovai, Neuro Comput. 43, 219 (2002)
Z. Wang, Y. Wang, Y. Liu, IEEE Trans. Neural Netw. 21, 11 (2010)
J.J. Collins, C.C. Chow, T.T. Imhoff, Nature 376, 236 (1995)
L.E. Abbott, C. van Vreeswijk, Phys. Rev. E 48, 1483 (1993)
H. Bolouri, E.H. Davidson, BioEssays 24, 1118 (2002)
H. De Jong, J. Comput. Biol. 9, 67 (2002)
F. Ren, J. Cao, Neurocomputing 71, 834 (2008)
D. Bray, J. Theor. Biol. 143, 215 (1990)
D. Alon, Science 301, 1866 (2003)
V. In, A.R. Bulsara, A. Palacios, P. Longhini, A. Kho, Phys. Rev. E 72, 045104 (2005)
B. Razavi, Fundamentals of Microelectronics (Wiley, New York, 2008)
A. Locquet, C. Masoller, C.R. Mirasso, Phys. Rev. E 65, 56205 (2002)
V. In, A. Kho, J.D. Neff, A. Palacios, P. Longhini, B.K. Meadows, Phys. Rev. Lett. 91, 244101 (2003)
A.R. Bulsara, V. In, A. Kho, P. Longhini, A. Palacios, W. Rappel, J. Acerbron, S. Baglio, B. Ando, Phys. Rev. E 70, 036103 (2004)
V. In, A.R. Bulsara, A. Palacios, P. Longhini, A. Kho, Phys. Rev. E 72, 045104 (2005)
J.F. Linder, A.R. Bulsara, Phys. Rev. E 74, 020105 (2006)
T. Dauxois, M. Payrard, Physics of Solitons (Cambridge University Press, Cambridge, 2006)
J.M. Carcione, Wave Fields in Inelastic, Porous and Electromagnetic Media (Elsevier, Amsterdam, 2007)
J.F. Lindner, K.M. Patton, P.M. Odenthal, J.C. Gallagher, B.J. Breen, Phys. Rev. E 78, 066604 (2008)
B.J. Breen, A.B. Doud, J.R. Grimm, A.H. Tanasse, S.J. Tanasse, J.E. Lindner, K.J. Maxted, Phys. Rev. E 83, 037601 (2011)
C. Yao, M. Zhan, Phys. Rev. E 81, 061129 (2010)
C. Jeevarathinam, S.Rajasekar, M.A.F. Sanjuan, Chaos 23, 013136 (2013)
S. Rajasekar, J. Used, A. Wagemakers, M.A.F. Sanjuan, Commun. Nonlinear Sci. Numer. Simul. 17, 3435 (2012)
M.B. Elowitz, S. Leibler, Nature 403, 335 (2000)
K.Y. Kim, D. Lepzelter, J. Wang, J. Chem. Phys. 126, 034702 (2007)
O. Buse, R. Perez, Phys. Rev. E 81, 066206 (2010)
S. Muller, J. Hofbauer, L. Endler, C. Flamm, S. Widder, P. Schuster, J. Math. Biol. 53, 905 (2006)
N. Strelkowa, M. Barahona, J. R. Soc. Interface 7, 1071 (2010)
N. Strelkowa, M. Barahona, Chaos 21, 023104 (2011)
S. Rajamani, S. Rajasekar, Phys. Scr. 88, 015010 (2013)
L.A. Pipes, L.R. Harvill, Applied Mathematics for Engineers and Physics (McGraw-Hill, New York, 1970)
J.F. Lindner, B.K. Meadows, W.L. Ditto, M.E. Inchisoa, A.R. Bulsara, Phys. Rev. Lett. 75, 3 (1995)
M. Locher, G.A. Johnson, E.R. Hunt, Phys. Rev. Lett. 77, 4698 (1996)
J.F. Lindner, B.K. Meadows, W.L. Ditto, M.E. Inchiosa, A.R. Bulsara, Phys. Rev. E 53, 2081 (1996)
N. Sungar, J.P. Sharpe, S. Weber, Phys. Rev. E 62, 1413 (2000)
O. Kwon, H.T. Moon, Phys. Lett. A 298, 319 (2002)
A. Pikovsky, A. Zaikin, M.A. de la Casa, Phys. Rev. Lett. 88, 050601 (2001)
M. Ozer, M. Uzuntarla, T. Kayikcioglu, L.J. Graham, Phys. Lett. A 372, 6498 (2008)
M. Perc, Phys. Rev. E 78, 036105 (2008)
M. Ozer, M. Perc, M. Uzuntarla, Phys. Lett. A 375, 965 (2009)
A. Zaikin, J. Kurths, L. Schimansky-Geier, Phys. Rev. Lett. 85, 227 (2000)
H. Hong, B.J. Kim, M.Y. Choi, Phys. Rev. E 66, 011107 (2002)
F.D. Duan, F. Chapeau-Blondeau, D. Abbott, Phys. Lett. A 372, 2159 (2008)
A. Krawiecki, Physica A 333, 505 (2004)
A. Krawiecki, Int. J. Mod. Phys. B 18, 1759 (2004)
A.L. Barabasi, R. Albert, Science 286, 509 (1999)
J.A. Acebron, S. Lozano, A. Arenas, Phys. Rev. Lett. 99, 128701 (2007)
D. Rousseau, F. Chapeau-Blondeau, Phys. Lett. A 321, 280 (2004)
P. McGraw, M. Menzinger, Phys. Rev. E 83, 037102 (2011)
T.S. Bellows, J. Anim. Ecol. 50, 139 (1981)
K. Masutani, Bull. Math. Biol. 55, 1 (1993)
S. Sinha, P.K. Das, Pramana J. Phys. 48, 87 (1997)
M. Perc, Phys. Rev. E 76, 066203 (2007)
M. Gosak, D. Korosak, M. Marhl, New J. Phys. 13, 013012 (2011)
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Rajasekar, S., Sanjuan, M.A.F. (2016). Signal Propagation in Unidirectionally Coupled Systems. In: Nonlinear Resonances. Springer Series in Synergetics. Springer, Cham. https://doi.org/10.1007/978-3-319-24886-8_7
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