Chimera and chimera-like states in populations of nonlocally coupled homogeneous and heterogeneous chemical oscillators

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

doi:10.1063/1.4962631

Cited by 57 publications

(22 citation statements)

References 44 publications

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“…The chemical micro-oscillators used in this study are catalyst-loaded cation-exchange beads in a catalyst-free BZ reaction mixture 10,18,[31][32][33] . To increase oscillator homogeneity, the particles (DOWEX WX4 100-200, diameters 75-150 μ m) were sieved to obtain a narrow size distribution of 106-112 μ m. The rutheniumtris-dimethylene-bipyridine ( + Ru(dmbpy) 3 2 ) catalyst was slowly added to 5.0 ml water containing 1.0 g of doubly-sieved beads and stirred with a vortex mixer for one day.…”

Section: Methodsmentioning

confidence: 99%

Spiral wave chimera states in large populations of coupled chemical oscillators

et al. 2017

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Section: Methodsmentioning

confidence: 99%

Spiral wave chimera states in large populations of coupled chemical oscillators

et al. 2017

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“…Moreover, it is also higher than the corresponding metastability index (λ γ ≈ 0.07). Therefore, we may indeed call the state "chimera-like" [38,54,[75][76][77][78].…”

Section: Communities Based On Dynamicsmentioning

confidence: 99%

Synchronization Patterns in Modular Neuronal Networks: A Case Study of C. elegans

Pournaki

Merfort

Ruiz

et al. 2019

Front. Appl. Math. Stat.

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We investigate synchronization patterns and chimera-like states in the modular multilayer topology of the connectome of Caenorhabditis elegans. In the special case of a designed network with two layers, one with electrical intra-community links and one with chemical inter-community links, chimera-like states are known to exist. Aiming at a more biological approach based on the actual connectivity data, we consider a network consisting of two synaptic (electrical and chemical) and one extrasynaptic (wireless) layers. Analyzing the structure and properties of this layered network using Multilayer-Louvain community detection, we identify modules whose nodes are more strongly coupled with each other than with the rest of the network. Based on this topology, we study the dynamics of coupled Hindmarsh-Rose neurons. Emerging synchronization patterns are quantified using the pairwise Euclidean distances between the values of all oscillators, locally within each community and globally across the network. We find a tendency of the wireless coupling to moderate the average coherence of the system: for stronger wireless coupling, the levels of synchronization decrease both locally and globally, and chimera-like states are not favored. By introducing an alternative method to define meaningful communities based on the dynamical correlations of the nodes, we obtain a structure that is dominated by two large communities. This promotes the emergence of chimera-like states and allows to relate the dynamics of the corresponding neurons to biological neuronal functions such as motor activities.

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“…For larger values of T r coherent double spots and stripe chimeras are formed, surrounded by the incoherent domains (Figure 8). In the top row of Figure 8 we can see the formation of a triple pattern (Figure 8A) composed by (i) a coherent stripe crossed by a traveling wave [57], (ii) an incoherent stripe surrounding the coherent region, while (iii) a third region consisting of traveling waves appears within the incoherent domain, at the top and bottom of the figure. The velocities of the traveling waves and the oscillator frequencies are different in the first and the third regions and this may support the idea of bistability.…”

Section: Random Fractal Connectivitymentioning

confidence: 99%

Chimera States With 2D Deterministic and Random Fractal Connectivity

Argyropoulos

Provata

2019

Front. Appl. Math. Stat.

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We study the formation of chimera states in 2D lattices with hierarchical (fractal) connectivity. The dynamics of the nodes follow the Leaky Integrate-and-Fire model and the connectivity has the form of a deterministic or a random Sierpinski carpet. We provide numerical evidence that for deterministic fractal connectivity and small values of the coupling strength, a hierarchical incoherent spot is produced with internal structure influenced by the fractal connectivity scheme. The spot size is similar to the size of the coupling matrix. Stable spots can be formed for symmetric fractal connectivity, while traveling ones are found when the connectivity matrix is asymmetric with respect to the center. For fractal coupling schemes spiral wave chimeras are produced and curious stable patterns are reported, which present triple coexistence of coherent regions, incoherent domains and traveling waves. In all cases, the coherent domains demonstrate the lowest mean phase velocities ω, the incoherent domains show intermediate ω-velocities, while the traveling waves show the highest ω-values. These findings confirm previous studies on symmetric deterministic hierarchical connectivities and extend here to slanted and random fractals.

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Chimera and chimera-like states in populations of nonlocally coupled homogeneous and heterogeneous chemical oscillators

Cited by 57 publications

References 44 publications

Spiral wave chimera states in large populations of coupled chemical oscillators

Spiral wave chimera states in large populations of coupled chemical oscillators

Synchronization Patterns in Modular Neuronal Networks: A Case Study of C. elegans

Chimera States With 2D Deterministic and Random Fractal Connectivity

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