Chimera States in Populations of Nonlocally Coupled Chemical Oscillators

Nkomo, Simbarashe; Tinsley, Mark R.; Showalter, Kenneth

doi:10.1103/physrevlett.110.244102

Cited by 276 publications

(190 citation statements)

References 24 publications

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“…In coupled nonlinear systems and networks time-delayed couplings represent an ubiquitous feature [18] which can also be used to control stability. Particular interest, besides the control of various synchronization patterns in networks of oscillators [19][20][21][22][23][24][25][26] has recently been paid to the suppression of oscillations through the coupling. There are two types of oscillation quenching known in the literature [27][28][29][30]: amplitude death and oscillation death.…”

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confidence: 99%

Time delay control of symmetry-breaking primary and secondary oscillation death

Zakharova¹,

Schneider²,

Kyrychko³

et al. 2013

EPL

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-We show that oscillation death as a specific type of oscillation suppression, which implies symmetry breaking, can be controlled by introducing time-delayed coupling. In particular, we demonstrate that time delay influences the stability of an inhomogeneous steady state, providing the opportunity to modulate the threshold for oscillation death. Additionally, we find a novel type of oscillation death representing a secondary bifurcation of an inhomogeneous steady state.Introduction. -Time-delayed couplings arise naturally in many types of networks, for instance in coupled lasers [1], neural networks [2-4], electronic circuits [5], or genetic oscillators [6], due to finite signal transmission and processing times, and memory and latency effects. While investigating real-world systems, it is necessary to take time delay into account, since the presence of time delay is an inherent property of the vast majority of processes that occur in nature [7,8]. Moreover, time-delayed coupling and feedback represent an important aspect of control [9]. Previous theoretical and experimental works have shown that time delay can be treated as a control parameter and can stabilize initially unstable states. In particular, time-delayed feedback has been used to stabilize unstable periodic orbits embedded in a deterministic chaotic attractor [10,11], or generated by a Hopf bifurcation [12], unstable steady states [13], spatio-temporal patterns [14][15][16], or control the coherence and timescales of stochastic motion [17]. In coupled nonlinear systems and networks time-delayed couplings represent an ubiquitous feature [18] which can also be used to control stability.

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confidence: 99%

Time delay control of symmetry-breaking primary and secondary oscillation death

Zakharova¹,

Schneider²,

Kyrychko³

et al. 2013

EPL

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“…In recent times several theoretical studies [16][17][18][19][20] and experimental investigations [21][22][23][24][25] have established chimera as a robust concept occurring in varied complex networks, including chaotic dynamical systems [21,26,27]. For example networks of chaotic dynamical systems with nonlocal coupling exhibit coexisting spatial domains of coherence and incoherence [26,27], coherent travelling waves [28] and spiral wave chimera states [29].…”

Section: Introductionmentioning

confidence: 99%

“…For example networks of chaotic dynamical systems with nonlocal coupling exhibit coexisting spatial domains of coherence and incoherence [26,27], coherent travelling waves [28] and spiral wave chimera states [29]. Experimentally they have been observed in optical [21] and chemical systems [22,23], a mechanical experiment consisting of two populations of metronomes [24] and a modified Ikeda time delay circuit system [25]. It has been recently pointed out [26,27] that transition from spatially coherent to incoherent state occurs via chimera state in models of coupled logistic map and Rössler systems with nonlocal interaction.…”

Section: Introductionmentioning

confidence: 99%

Observation and characterization of chimera states in coupled dynamical systems with nonlocal coupling

Gopal

Chandrasekar

Venkatesan³

et al. 2014

Phys. Rev. E

169

160

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By developing the concepts of strength of incoherence and discontinuity measure, we show that a distinct quantitative characterization of chimera and multichimera states which occur in networks of coupled nonlinear dynamical systems admitting nonlocal interactions of finite radius can be made. These measures also clearly distinguish between chimera/multichimera states (both stable and breathing types) and coherent and incoherent as well as cluster states. The measures provide a straight forward and precise characterization of the various dynamical states in coupled chaotic dynamical systems irrespective of the complexity of the underlying attractors.

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“…Recently, a state with a counterintuitive structure, usually referred to as a "chimera state", was discovered in numerical simulations of nonlocally coupled oscillator arrays 15 . Since then, an intense theoretical [16][17][18][19][20][21][22][23][24][25][26][27][28][29] and experimental [30][31][32][33][34][35][36][37][38][39][40] activity has been initiated. A "chimera state" is characterized by the coexistence of synchronous and asynchronous clusters (subgroups) of oscillators, even though they are coupled symmetrically and they are identical 41,42 .…”

Section: Introductionmentioning

confidence: 99%

Chimeras in SQUID metamaterials

2015

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Regular lattices comprising Superconducting QUantum Interference Devices (SQUIDs) form magnetic metamaterials exhibiting extraordinary properties, including tuneability, dynamic multistability, and negative magnetic permeability. The SQUIDs in a metamaterial interact through non-local, magnetic dipole-dipole forces, that makes it possible for counter-intuitive dynamic states referred to as chimera states to appear; the latter feature clusters of SQUIDs with synchronous dynamics which coexist with clusters exhibiting asynchronous behavior. The spontaneous appearence of chimera states is demonstrated numerically for one-dimensional SQUID metamaterials driven by an alternating magnetic field in which the fluxes threading the SQUID rings are randomly initialized; then, chimera states appear generically for sufficiently strong initial excitations, which exhibit relatively long life-times. The synchronization and metastability levels of the chimera states are discussed in terms of appropriate measures. Given that both one-and two-dimensional SQUID metamaterials have been already fabricated and investigated in the lab, the presence of a chimera state could in principle be detected with presently available experimental set-ups.

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Chimera States in Populations of Nonlocally Coupled Chemical Oscillators

Cited by 276 publications

References 24 publications

Time delay control of symmetry-breaking primary and secondary oscillation death

Time delay control of symmetry-breaking primary and secondary oscillation death

Observation and characterization of chimera states in coupled dynamical systems with nonlocal coupling

Chimeras in SQUID metamaterials

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