Abstract:
We consider in detail similarities and differences of the “coherence–incoherence” transition in ensembles of nonlocally coupled chaotic discrete-time systems with nonhyperbolic and hyperbolic attractors. As basic models we employ the Hénon map and the Lozi map. We show that phase and amplitude chimera states appear in a ring of coupled Hénon maps, while no chimeras are observed in an ensemble of coupled Lozi maps. In the latter, the transition to spatio-temporal chaos occurs via solitary states. We present numerical results for the coupling function which describes the impact of neighboring oscillators on each partial element of an ensemble with nonlocal coupling. Varying the coupling strength we analyze the evolution of the coupling function and discuss in detail its role in the “coherence–incoherence” transition in the ensembles of Hénon and Lozi maps.
Keywords:
ensemble of nonlocally coupled oscillators, chimera states, solitary states, hyperbolic and nonhyperbolic attractors, coupling function.
Citation:
Nadezhda I. Semenova, Elena V. Rybalova, Galina I. Strelkova, Vadim S. Anishchenko, ““Coherence–incoherence” Transition in Ensembles of Nonlocally Coupled Chaotic Oscillators with Nonhyperbolic and Hyperbolic Attractors”, Regul. Chaotic Dyn., 22:2 (2017), 148–162
\Bibitem{SemRybStr17}
\by Nadezhda I. Semenova, Elena V. Rybalova, Galina I. Strelkova, Vadim S. Anishchenko
\paper “Coherence–incoherence” Transition in Ensembles of Nonlocally Coupled Chaotic Oscillators with Nonhyperbolic and Hyperbolic Attractors
\jour Regul. Chaotic Dyn.
\yr 2017
\vol 22
\issue 2
\pages 148--162
\mathnet{http://mi.mathnet.ru/rcd248}
\crossref{https://doi.org/10.1134/S1560354717020046}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85016985240}
Linking options:
https://www.mathnet.ru/eng/rcd248
https://www.mathnet.ru/eng/rcd/v22/i2/p148
This publication is cited in the following 25 articles:
A. D. Ryabchenko, E. V. Rybalova, G. I. Strelkova, “Vozdeistvie additivnogo shuma na khimernye i uedinennye sostoyaniya v neironnykh ansamblyakh”, Izvestiya vuzov. PND, 32:1 (2024), 121–140
E. Rybalova, V. Averyanov, R. Lozi, G. Strelkova, “Peculiarities of the spatio-temporal dynamics of a Hénon–Lozi map network in the presence of Lévy noise”, Chaos, Solitons & Fractals, 184 (2024), 115051
Elena Rybalova, Eckehard Schöll, Galina Strelkova, “Controlling chimera and solitary states by additive noise in networks of chaotic maps”, Journal of Difference Equations and Applications, 29:9-12 (2023), 909
E. Rybalova, S. Muni, G. Strelkova, “Transition from chimera/solitary states to traveling waves”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 33:3 (2023)
Elena Rybalova, Vasilii Nechaev, Eckehard Schöll, Galina Strelkova, “Chimera resonance in networks of chaotic maps”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 33:9 (2023)
Elena Rybalova, Galina Strelkova, “Response of solitary states to noise-modulated parameters in nonlocally coupled networks of Lozi maps”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 32:2 (2022)
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E. V. Rybalova, A. Zakharova, G. I. Strelkova, “Interplay between solitary states and chimeras in multiplex neural networks”, Chaos Solitons Fractals, 148 (2021), 111011
R. G. Andrzejak, “Chimeras confined by fractal boundaries in the complex plane”, Chaos, 31:5 (2021), 053104
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E. V. Rybalova, G. I. Strelkova, V. S. Anishchenko, “Impact of sparse inter-layer coupling on the dynamics of a heterogeneous multilayer network of chaotic maps”, Chaos Solitons Fractals, 142 (2021), 110477
E. Rybalova, G. Strelkova, E. Schoell, V. Anishchenko, “Relay and complete synchronization in heterogeneous multiplex networks of chaotic maps”, Chaos, 30:6 (2020)
R. G. Andrzejak, G. Ruzzene, E. Schoell, I. Omelchenko, “Two populations of coupled quadratic maps exhibit a plentitude of symmetric and symmetry broken dynamics”, Chaos, 30:3 (2020), 033125
G. I. Strelkova, V. S. Anishchenko, “Spatio-temporal structures in ensembles of coupled chaotic systems”, Phys. Usp., 63:2 (2020), 145–161
Elena V. Rybalova, Daria Y. Klyushina, Vadim S. Anishchenko, Galina I. Strelkova, “Impact of Noise on the Amplitude Chimera Lifetime in an Ensemble of Nonlocally Coupled Chaotic Maps”, Regul. Chaotic Dyn., 24:4 (2019), 432–445
E. Teichmann, M. Rosenblum, “Solitary states and partial synchrony in oscillatory ensembles with attractive and repulsive interactions”, Chaos, 29:9 (2019), 093124
E. Rybalova, V. S. Anishchenko, G. I. Strelkova, A. Zakharova, “Solitary states and solitary state chimera in neural networks”, Chaos, 29:7 (2019), 071106
V. S. Anishchenko, G. I. Strelkova, “Chimera structures in the ensembles of nonlocally coupled chaotic oscillators”, Radiophys. Quantum Electron., 61:8-9 (2019), 659–671
M. P. Kulakov, E. Ya. Frisman, “Klasterizatsiya i khimery v modeli prostranstvenno-vremennoi dinamiki populyatsii s vozrastnoi strukturoi”, Nelineinaya dinam., 14:1 (2018), 13–31
N. Semenova, T. Vadivasova, V. Anishchenko, “Mechanism of solitary state appearance in an ensemble of nonlocally coupled Lozi maps”, Eur. Phys. J.-Spec. Top., 227:10-11 (2018), 1173–1183
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