Abstract
We study how the phenomenon of response to synchronization arises in sets of pulse-coupled dissimilar oscillators. One of the sets is constituted by oscillators that can easily synchronize. Conversely, the oscillators of the other set do not synchronize. When the elements of the first set are not synchronized, they induce oscillation death in the constituents of the second set. By contrast, when synchronization is achieved in oscillators of the first set, those of the second set recover their oscillatory behavior and thus, responding to synchronization. Additionally, we found another interesting phenomenon in this type of systems, namely, a new control of simultaneous firings in a population of similar oscillators attained by means of the action of a dissimilar oscillator.
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References
I. Blekhman, Vibrational Mechanics: Nonlinear Dynamic Effects, General Approach, Applications (World Scientific, Singapore, 2000)
I.I. Blekhman, Synchronization in Science and Technology (ASME Press, New York, 1988)
A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization: a Universal Concept in Nonlinear Sciences (Cambridge University Press, New York, 2001)
S. Boccaletti, L.M. Pecora, A. Pelaez, Phys. Rev. E 63, 066219 (2001)
H. Nijmeije, A. Rodriguez-Angeles, Synchronization of Mechanical Systems (World Scientific, Singapore, 2003)
A. Stefanski, Determining Thresholds of Complete Synchronization, and Application (World Scientific, 2009)
H. Fukuda, H. Morimura, S. Kai, Physica D 205, 80 (2005)
M. Lara-Aparicio, C. Barriga-Montoya, P. Padilla-Longoria, B. Fuentes-Pardo, Math. Biosci. Eng. 11, 317 (2014)
J. Gonzalez-Miranda, Synchronization And Control Of Chaos: An Introduction For Scientists And Engineers (Imperial College Press, London, 2004)
X.B. Lu, B.Z. Qin, Synchronization in Complex Networks (Nova Science, New York, 2011)
A.E. Motter, S.A. Myers, M. Anghel, T. Nishikawa, Nat. Phys. 9, 191 (2013)
G. Grinstein, R. Linsker, P. Natl. Acad. Sci. USA 102, 9948 (2005)
W. Zhou, J. Yang, L. Zhou, D. Tong, Stability and Synchronization Control of Stochastic Neural Networks (Springer, Berlin, 2016)
L. Kocarev, Consensus and Synchronization in Complex Networks (Springer, Berlin, 2013)
R. Bader, Nonlinearities and Synchronization in Musical Acoustics and Music Psychology (Springer, Heidelberg, 2013)
S. Boccaletti, J. Kurths, G. Osipov, D.L. Valladares, C.S. Zhou, Phys. Rep. 366, 1 (2002)
S.C. Manrubia, A.S. Mikhailov, D.H. Zanette, Emergence of Dynamical Order (World Scientific, Singapore, 2004)
S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.U. Hwang, Phys. Rep. 424, 175 (2006)
A. Balanov, N. Janson, D. Postnov, O. Sosnovtseva, Synchronization: From Simple to Complex (Springer, Berlin, 2007)
S. Boccaletti, The Synchronized Dynamics of Complex Systems (Elsevier, New York, 2008)
J.A. Acebron, L.L. Bonilla, C.J.P. Vicente, F. Ritort, R. Spigler, Rev. Mod. Phys. 77, 137 (2005)
F.A. Rodrigues, T.K.D.M. Peron, P. Ji, J. Kurths, Phys. Rep. 610, 1 (2016)
Y. Kuramoto, Physica D 50, 15 (1991)
S. Bottani, Phys. Rev. E 54, 2334 (1996)
G.M. Ramírez Ávila, J. Kurths, J.L. Guisset, J.L. Deneubourg, Eur. Phys. J. Special Topics 223, 2759 (2014)
A.N. Pisarchik, U. Feudel, Phys. Rep. 540, 167 (2014)
W. Zou, D.V. Senthilkumar, J. Duan, J. Kurths, Phys. Rev. E 90, 032906 (2014)
F.M. Atay, Physica D 183, 1 (2003)
T. Banerjee, D. Biswas, Chaos 23, 043101 (2013)
A. Koseska, E. Volkov, J. Kurths, Chaos 20, 023132 (2010)
A. Koseska, E. Volkov, J. Kurths, Phys. Rep. 531, 173 (2013)
A. Koseska, E. Volkov, J. Kurths, Phys. Rev. Lett. 111, 024103 (2013)
J. Buck, E. Buck, Science 159, 1319 (1968)
J. Copeland, A. Moiseff, J. Insect Physiol. 43, 965 (1997)
A. Moiseff, J. Copeland, J. Insect Behav. 13, 597 (2000)
N. Ohba, Integr. Comp. Biol. 44, 225 (2004)
A.T. Winfree, J. Theor. Biol. 16, 15 (1967)
R.E. Mirollo, S.H. Strogatz, SIAM J. Appl. Math. 50, 1645 (1990)
G.M. Ramírez Ávila, J.L. Guisset, J.L. Deneubourg, Physica D 182, 254 (2003)
J. Buck, J.F. Case, Biol. Bull. 121, 234 (1961)
A. Moiseff, J. Copeland, Science 329, 181 (2010)
G.M. Ramírez Ávila, J.L. Deneubourg, J.L. Guisset, N. Wessel, J. Kurths, Europhys. Lett. 94, 60007 (2011)
T. Buschmann, A. Ewald, A. von Twickel, A. Bschges, Bioinspir. Biomim. 10, 041001 (2015)
B.V.C. Martins, G. Brunetto, F. Sato, V.R. Coluci, D.S. Galvão, Chem. Phys. Lett. 453, 290 (2008)
J. Buck, E. Buck, Am. Nat. 112, 471 (1978)
W. Woods Jr, H. Hendrickson, J. Mason, S. Lewis, Am. Nat. 170, 702 (2007)
E. Izhikevich, Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting (MIT Press, Cambridge, 2007)
P. Schultz, T. Peron, D. Eroglu, T. Stemler, G.M. Ramírez Ávila, F.A. Rodrigues, J. Kurths, Phys. Rev. E 93, 062211 (2016)
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Ramírez-Ávila, G.M., Kurths, J. Unraveling the primary mechanisms leading to synchronization response in dissimilar oscillators. Eur. Phys. J. Spec. Top. 225, 2487–2506 (2016). https://doi.org/10.1140/epjst/e2016-60033-5
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DOI: https://doi.org/10.1140/epjst/e2016-60033-5