Effects of different initial conditions on the emergence of chimera states

Faghani, Zahra; Arab, Zahra; Parastesh, Fatemeh; Jafari, Sajad; Perc, Matjaž; Slavinec, Mitja

doi:10.1016/j.chaos.2018.07.023

Cited by 44 publications

(13 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The literature on chaos in networks is plenty of works [106][107][108][109][110][111][112][113][114][115][116]. The interest has been even amplified after the discovery of the chimera states and many other works have been devoted to such study [117][118][119][120][121][122][123][124][125][126][127]. Nevertheless, computational chaos in complex networks has received much less attention.…”

Section: Introductionmentioning

confidence: 99%

Computational chaos in complex networks

Nepomuceno

Perc

2019

Journal of Complex Networks

Self Cite

View full text Add to dashboard Cite

Computational chaos reports the artificial generation or suppression of chaotic behaviour in digital computers. There is a significant interest of the scientific community in analysing and understanding computational chaos of discrete and continuous systems. Notwithstanding, computational chaos in complex networks has received much less attention. In this article, we report computational chaos in a network of coupled logistic maps. We consider two types of networks, namely the Erdös-Rényi random network and the Barabási-Albert scale-free network. We show that there is an emergence of computational chaos when two different natural interval extensions are used in the simulation. More surprisingly, we also show that this chaos can be suppressed by an average of natural interval extensions, which can thus be considered as a filter to reduce the uncertainty stemming from the inherent finite precision of computer simulations.

show abstract

Section: Introductionmentioning

confidence: 99%

Computational chaos in complex networks

Nepomuceno

Perc

2019

Journal of Complex Networks

Self Cite

View full text Add to dashboard Cite

show abstract

“…In fact, we found that the chimera region broadens in the parameter space with the increase of the non-pairwise interaction strength. The influence of initial conditions have already been well established in the literature for the emergence of chimera states in pairwise interacting network [63][64][65][66]. Here, we observe that the variation of initial conditions in presence of higher-order inetractions promotes the coexistence of multiple states, which are characterized by quantifying the basin stability of those states.…”

mentioning

confidence: 64%

Higher-order interactions promote chimera states

Kundu,

Ghosh

2022

Preprint

View full text Add to dashboard Cite

Since the discovery of chimera states, the presence of a nonzero phase lag parameter turns out to be an essential attribute for the emergence of chimeras in a nonlocally coupled identical Kuramoto phase oscillators' network with pairwise interactions. In this letter, we report the emergence of chimeras without phase lag in nonlocally coupled identical Kuramoto network owing to the introduction of non-pairwise interactions. The influence of added nonlinearity in the coupled system dynamics in the form of simplicial complexes mitigates the requisite of a nonzero phase lag parameter for the emergence of chimera states. Chimera states stimulated by the reciprocity of the pairwise and non-pairwise interaction strengths and their multistable nature are characterized with appropriate measures and are demonstrated in the parameter spaces.

show abstract

“…), and their sensitivity to the initial conditions that make their experimental verification difficult to achieve. 4,9,25 Outstanding theoretical results have been obtained in the study of chimeras, and promising methods have been proposed to reveal the mystery surrounding these exotic states, such as whether they will exist, their stability, and, especially, their origin. For example, it has been found that chimeras are stable in infinite-size networks and that they can be transient in finite ones.…”

Section: Introductionmentioning

confidence: 99%

Symmetry-breaking mechanism for the formation of cluster chimera patterns

Asllani

Siebert

Arenas

et al. 2022

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

The emergence of order in collective dynamics is a fascinating phenomenon that characterizes many natural systems consisting of coupled entities. Synchronization is such an example where individuals, usually represented by either linear or nonlinear oscillators, can spontaneously act coherently with each other when the interactions' configuration fulfills certain conditions. However, synchronization is not always perfect, and the coexistence of coherent and incoherent oscillators, broadly known in the literature as chimera states, is also possible. Although several attempts have been made to explain how chimera states are created, their emergence, stability, and robustness remain a long-debated question. We propose an approach that aims to establish a robust mechanism through which cluster synchronization and chimera patterns originate. We first introduce a stability-breaking method where clusters of synchronized oscillators can emerge. At variance with the standard approach where synchronization arises as a collective behavior of coupled oscillators, in our model, the system initially sets on a homogeneous fixedpoint regime, and, only due to a global instability principle, collective oscillations emerge. Following a combination of the network modularity and the model's parameters, one or more clusters of oscillators become incoherent within yielding a particular class of patterns that we here name cluster chimera states.

show abstract

Effects of different initial conditions on the emergence of chimera states

Cited by 44 publications

References 29 publications

Computational chaos in complex networks

Computational chaos in complex networks

Higher-order interactions promote chimera states

Symmetry-breaking mechanism for the formation of cluster chimera patterns

Contact Info

Product

Resources

About