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A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences ( Cambridge University Press, Cambridge, 2001).
M. Wickramasinghe and I. Z. Kiss, “ Synchronization of electrochemical oscillators,” in Engineering of Chemical Complexity, edited by A. S. Mikhailov and G. Ertl ( Wolrd Scientific, 2013), pp. 215236.
K. Bar-Eli and S. Reuveni, “ Stable stationary states of coupled chemical oscillators. Experimental evidence,” J. Phys. Chem. 89, 13291330 (1985).
M. F. Crowley and I. R. Epstein, “ Experimental and theoretical studies of a coupled chemical oscillator: Phase death, multistability, and in-phase and out-of-phase entrainment,” J. Phys. Chem. 93, 24962502 (1989).
M. Yoshimoto, “ Phase-death mode in two-coupled chemical oscillators studied with reactors of different volume and by simulation,” Chem. Phys. Lett. 280, 539543 (1997).
S. Jain, I. Z. Kiss, J. Breidenich, and J. L. Hudson, “ The effect of IR compensation on stationary and oscillatory patterns in dual-electrode metal dissolution systems,” Electrochim. Acta 55, 363373 (2009).
Y. Zhai, I. Z. Kiss, and J. L. Hudson, “ Amplitude death through a Hopf bifurcation in coupled electrochemical oscillators: Experiments and simulations,” Phys. Rev. E 69, 026208 (2004).
R. Herrero, M. Figueras, J. Rius, F. Pi, and G. Orriols, “ Experimental observation of the amplitude death effect in two coupled nonlinear oscillators,” Phys. Rev. Lett. 84, 53125315 (2000).
D. V. Ramana Reddy, A. Sen, and G. L. Johnston, “ Experimental evidence of time-delay-induced death in coupled limit-cycle oscillators,” Phys. Rev. Lett. 85, 33813384 (2000).
T. Banerjee and D. Ghosh, “ Experimental observation of a transition from amplitude to oscillation death in coupled oscillators,” Phys. Rev. E 89, 062902 (2014).
G. B. Ermentrout and N. Kopell, “ Oscillator death in systems of coupled neural oscillators,” SIAM J. Math. Anal. 50, 125 (1990).
D. G. Aronson, G. B. Ermentrout, and N. Kopell, “ Amplitude response of coupled oscillators,” Physica D 41, 403449 (1990).
A. Koseska, E. Volkov, and J. Kurths, “ Transition from amplitude to oscillation death via Turing bifurcation,” Phys. Rev. Lett. 111, 024103 (2013).
G. Saxena, A. Prasad, and R. Ramaswamy, “ Amplitude death: The emergence of stationarity in coupled nonlinear systems,” Phys. Rep. 521, 205 (2012).
A. Koseska, E. Volkov, and J. Kurths, “ Oscillation quenching mechanisms: Amplitude vs. oscillation death,” Phys. Rep. 531, 173 (2013).
K. Bar-Eli, “ Oscillations death revisited; coupling of identical chemical oscillators,” Phys. Chem. Chem. Phys. 13, 1160611614 (2011).
K. Konishi, “ Limitation of time-delay induced amplitude death,” Phys. Lett. A 341, 401409 (2005).
W. Zou, C. Yao, and M. Zhan, “ Eliminating delay-induced oscillation death by gradient coupling,” Phys. Rev. E 82, 056203 (2010).
W. Zou, D. V. Senthilkumar, M. Zhan, and J. Kurths, “ Reviving oscillations in coupled nonlinear oscillators,” Phys. Rev. Lett. 111, 014101 (2013).
W. Zou, D. V. Senthilkumar, R. Nagao, I. Z. Kiss, Y. Tang, A. Koseska, J. Duan, and J. Kurths, “ Restoration of rhythmicity in diffusively coupled dynamical networks,” Nat. Commun. 6, 7709 (2015).
D. Ghosh, T. Banerjee, and J. Kurths, “ Revival of oscillation from mean-field-induced death: Theory and experiment,” Phys. Rev. E 92, 052908 (2015).
W. Hohmann, N. Schinor, M. Kraus, and F. W. Schneider, “ Electrically coupled chemical oscillators and their action potentials,” J. Phys. Chem. A 103, 57425748 (1999).
V. Horvath, P. L. Gentili, V. K. Vanag, and I. R. Epstein, “ Pulse-coupled chemical oscillators with time delay,” Angew. Chem. Int. Ed. 51, 68786881 (2012).
V. Votrubova, P. Hasal, L. Schreiberova, and M. Marek, “ Dynamical patterns in arrays of coupled chemical oscillators and excitators,” J. Phys. Chem. A 102, 13181328 (1998).
J. Delgado, N. Li, M. Leda, H. O. Gonzalez-Ochoa, S. Fraden, and I. R. Epstein, “ Coupled oscillations in a 1D emulsion of Belousov-Zhabotinsky droplets,” Soft Matter 7, 31553167 (2011).
M. Toiya, H. O. Gonzalez-Ochoa, V. K. Vanag, S. Fraden, and I. R. Epstein, “ Synchronization of chemical micro-oscillators,” J. Phys. Chem. Lett. 1, 12411246 (2010).
M. Toiya, V. K. Vladimir, and I. R. Epstein, “ Diffusively coupled chemical oscillators in a microfluidic assembly,” Angew. Chem. Int. Ed. 47, 77537755 (2008).
N. Tompkins, N. Li, C. Girabawe, M. Heymann, G. B. Ermentrout, I. R. Epstein, and S. Fraden, “ Testing Turing's theory of morphogenesis in chemical cells,” Proc. Natl. Acad. Sci. U.S.A. 111, 43974402 (2014).
S. Nkomo, M. R. Tinsley, and K. Showalter, “ Chimera states in populations of nonlocally coupled chemical oscillators,” Phys. Rev. Lett. 110, 244102 (2013).
M. R. Tinsley, S. Nkomo, and K. Showalter, “ Chimera and phase-cluster states in populations of coupled chemical oscillators,” Nat. Phys. 8, 662665 (2012).
A. F. Taylor, M. R. Tinsley, F. Wang, and K. Showalter, “ Phase clusters in large populations of chemical oscillators,” Angew. Chem. Int. Ed. 50, 1016110164 (2011).
A. F. Taylor, M. R. Tinsley, F. Wang, Z. Y. Huang, and K. Showalter, “ Dynamical quorum sensing and synchronization in large populations of chemical oscillators,” Science 323, 614617 (2009).
R. Makki, A. P. Munuzuri, and J. Perez-Mercader, “ Periodic perturbation of chemical oscillators: Entrainment and induced synchronization,” Chem. Eur. J. 20, 1421314217 (2014).
P. Kumar, D. K. Verma, P. Parmananda, and S. Boccaletti, “ Experimental evidence of explosive synchronization in mercury beating-heart oscillators,” Phys. Rev. E 91, 062909 (2015).
M. Wickramasinghe and I. Z. Kiss, “ Spatially organized dynamical states in chemical oscillator networks: Synchronization, dynamical differentiation, and chimera patterns,” PLoS One 8, e80586 (2013).
J. Nawrath, M. C. Romano, M. Thiel, I. Z. Kiss, M. Wickramasinghe, J. Timmer, J. Kurths, and B. Schelter, “ Distinguishing direct from indirect interactions in oscillatory networks with multiple time scales,” Phys. Rev. Lett. 104, 038701 (2010).
I. Z. Kiss, Y. M. Zhai, and J. L. Hudson, “ Emerging coherence in a population of chemical oscillators,” Science 296, 16761678 (2002).
K. Blaha, J. Lehnert, A. Keane, T. Dahms, P. Hövel, E. Schöll, and J. L. Hudson, “ Clustering in delay-coupled smooth and relaxational chemical oscillators,” Phys. Rev. E 88, 062915 (2013).
A. Karantonis, Y. Miyakita, and S. Nakabayashi, “ Synchronization of coupled assemblies of relaxation oscillatory electrode pairs,” Phys. Rev. E 65, 046213 (2002).
M. Sebek, R. Toenjes, and I. Z. Kiss, “ Complex rotating waves and long transients in a ring network of electrochemical oscillators with sparse random cross-connections,” Phys. Rev. Lett. 116, 068701 (2016).
M. Wickramasinghe and I. Z. Kiss, “ Spatially organized partial synchronization through the chimera mechanism in a network of electrochemical reactions,” Phys. Chem. Chem. Phys. 16, 1836018369 (2014).
M. Yoshimoto, K. Yoshikawa, and Y. Mori, “ Coupling among three chemical oscillators: Synchronization, phase death, and frustration,” Phys. Rev. E 47, 864874 (1993).
Y. Zhai, I. Z. Kiss, and J. L. Hudson, “ Control of complex dynamics with time-delayed feedback in populations of chemical oscillators: Desynchronization and clustering,” Ind. Eng. Chem. Res. 47, 35023514 (2008).
F. M. Atay, “ Oscillator death in coupled functional differential equations near Hopf bifurcation,” J. Differ. Equations 221, 190 (2006).
W. Michiels and H. Nijmeier, “ Synchronization of delay-coupled nonlinear oscillators: An approach based on the stability analysis of synchronized equilibria,” Chaos 19, 033110 (2009).
J. K. Hale, Functional Differential Equations ( Springer, New York, 1971).
M. P. Mehta and A. Sen, “ Death island boundaries for delay-coupled oscillator chains,” Phys. Lett. A 355, 202206 (2006).
I. Z. Kiss, Z. Kazsu, and V. Gáspár, “ Tracking unstable steady states and periodic orbits of oscillatory and chaotic electrochemical systems using delayed feedback control,” Chaos 16, 033109 (2006).
W. Zou, X. Zheng, and M. Zhan, “ Insensitive dependence of delay-induced oscillation death on complex networks,” Chaos 21, 023130 (2011).
H. Varela, C. Beta, A. Bonnefont, and K. Krischer, “ A hierarchy of global coupling induced cluster patterns during the oscillatory H2-electrooxidation reaction on a Pt ring-electrode,” Phys. Chem. Chem. Phys. 7, 24292439 (2005).

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The dynamical behavior of delay-coupled networks of electrochemical reactions is investigated to explore the formation of amplitude death (AD) and the synchronization states in a parameter region around the amplitude death region. It is shown that difference coupling with odd and even numbered ring and random networks can produce the AD phenomenon. Furthermore, this AD can be restored by changing the coupling type from difference to direct coupling. The restored oscillations tend to create synchronization patterns in which neighboring elements are in nearly anti-phase configuration. The ring networks produce frozen and rotating phase waves, while the random network exhibits a complex synchronization pattern with interwoven frozen and propagating phase waves. The experimental results are interpreted with a coupled Stuart-Landau oscillator model. The experimental and theoretical results reveal that AD behavior is a robust feature of delayed coupled networks of chemical units; if an oscillatory behavior is required again, even a small amount of direct coupling could be sufficient to restore the oscillations. The restored nearly anti-phase oscillatory patterns, which, to a certain extent, reflect the symmetry of the network, represent an effective means to overcome the AD phenomenon.


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