Chimera and phase-cluster states in populations of coupled chemical oscillators

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

doi:10.1038/nphys2371

Cited by 670 publications

(508 citation statements)

References 29 publications

Supporting

Mentioning

495

Contrasting

Unclassified

Order By: Relevance

“…Finally, we note that such chemically initiated communication is not restricted to just BZ gels, and is observed in other heterogeneous BZ systems. [72][73][74][75][76][77] The experiments performed by Yoshida et al 68 provided the first evidence that the dynamic behavior of a system of many self-oscillating BZ gels could be engineered by tailoring the shape and spatial arrangement of the constituent pieces. The fabrication technique developed in the latter study opened a new route to creating novel biomimetic chemomechanical devices based on the self-oscillating gels.…”

Section: Passage Of Chemo-mechanical Waves Through Adjacent Samplesmentioning

confidence: 99%

Chemo-responsive, self-oscillating gels that undergo biomimetic communication

et al. 2013

View full text Add to dashboard Cite

Species ranging from single-cell organisms to social insects can undergo auto-chemotaxis, where the entities move towards a chemo-attractant that they themselves emit. Polymer gels undergoing the self-oscillating Belousov-Zhabotinsky (BZ) reaction exhibit autonomous, periodic pulsations, which produce chemical species collectively referred to as the activator. The diffusion of this activator into the surrounding solution affects the dynamic behavior of neighboring BZ gels and hence, the BZ gels not only emit, but also respond to self-generated chemical gradients. This review describes recent experimental and computational studies that reveal how this biomimetic behavior effectively allows neighboring BZ gels to undergo cooperative, self-propelled motion. These distinctive properties of the BZ gels provide a route for creating reconfigurable materials that autonomously communicate with neighboring units and thereby actively participate in constructing the desired structures.

show abstract

Section: Passage Of Chemo-mechanical Waves Through Adjacent Samplesmentioning

confidence: 99%

Chemo-responsive, self-oscillating gels that undergo biomimetic communication

et al. 2013

View full text Add to dashboard Cite

show abstract

“…For p > 1 (known as strong delay kernel in the case p = 2), the biggest influence on the coupling at any moment of time t is from the values of z 1,2 at t − (p − 1)/α. The delay distribution (2.14) has the mean time delay 15) and the variance…”

Section: (B) Gamma Distribution Kernelmentioning

confidence: 99%

“…Recent work on laser communication networks has extensively used coupled oscillator models to study the dynamics of in-phase or anti-phase and complete chaos synchronization [6][7][8][9][10]. Chimera states, where a network of oscillators splits into coexisting domains of coherent, phaselocked and incoherent, desynchronized behaviour, have also been observed [11][12][13][14][15]. These studies have shown that coupling between different elements can play a dual role in the dynamics: it can both lead to suppression of oscillations and also facilitate a certain degree of synchronization between different elements.…”

Section: Introductionmentioning

confidence: 99%

Amplitude and phase dynamics in oscillators with distributed-delay coupling

Kyrychko

Blyuss

Schöll

2013

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

This paper studies the effects of distributed-delay coupling on the dynamics in a system of non-identical coupled Stuart–Landau oscillators. For uniform and gamma delay distribution kernels, the conditions for amplitude death are obtained in terms of average frequency, frequency detuning and the parameters of the coupling, including coupling strength and phase, as well as the mean time delay and the width of the delay distribution. To gain further insights into the dynamics inside amplitude death regions, the eigenvalues of the corresponding characteristic equations are computed numerically. Oscillatory dynamics of the system is also investigated, using amplitude and phase representation. Various branches of phase-locked solutions are identified, and their stability is analysed for different types of delay distributions.

show abstract

“…[1,2] Similarly, recent advances in microfabrication allow the generation of engineered networks of reaction units, e.g., with labon-chip microdroplets, [3] electrode arrays, [4,5] BZ beads, [6] or microelectrofusion. [7] The interplays between local reaction kinetics (nodes), the physical processes that create coupling (link), and the architecture of the network in such systems can lead to a wealth of self-organized phenomena, including synchronization, [4,6,8] stationary Turing and oscillatory patterns, [9,10,11,12,13] or excitation waves. [14,15,16] Stationary patterns generated via the Turing [17] mechanism have been observed in experiments for both continuous [18] and networked [19] systems.…”

mentioning

confidence: 99%

Self‐Organized Stationary Patterns in Networks of Bistable Chemical Reactions

et al. 2016

View full text Add to dashboard Cite

Experiments with a network of bistable electrochemical reactions, organized in regular and non-regular tree networks, are presented to confirm an alternative to Turing mechanism for formation selforganized stationary patterns. The results show that the pattern formation can be described by identification of domains that can be activated individually or in combinations. The method was also demonstrated to localization of chemical reactions to network substructures and identification of critical sites whose activation results in complete activation of the system. While the experiments were performed with a specific nickel electrodissolution system, they reproduce all the salient dynamical behavior of a general network model with a single nonlinearity parameter. This indicates that the considered pattern formation mechanism is very robust and similar behavior can thus be expected in other natural or engineered networked systems, which exhibit, at least locally, a tree-like structure.In biological context, many chemical reactions take place in discrete units, e.g., in cells, that form a complex network. The interplays between local reaction kinetics (nodes), the physical processes that create coupling (link), and the architecture of the network in such systems can lead to a wealth of self-organized phenomena, including synchronization, [4,6,8] stationary Turing and oscillatory patterns, [9,10,11,12,13] or excitation waves. [14,15,16] Stationary patterns generated via the Turing[17] mechanism have been observed in experiments for both continuous [18] and networked [19] systems. Here, an alternative mechanism for emergence of stationary patterns in networks is experimentally explored. We focus on network-organized systems of bistable elements with diffusive connections between them. Bistable elements can be found in a broad class of chemical reactions (e.g., with autocatalysis [20,21]) but also in cellular [22] and engineered systems.[23] Such elements can have local or diffusive connections between them. For regular lattices and linear chains (i.e., for relatively simple networks), it is known that, under sufficiently weak coupling, the fronts fail to propagate, and thus stationary domains can be formed, [24,25,26,27] whereas at strong coupling the fronts spread [27,28] and a uniform state is eventually established. Recently, analogues phenomena were theoretically investigated for complex 1

show abstract

Chimera and phase-cluster states in populations of coupled chemical oscillators

Cited by 670 publications

References 29 publications

Chemo-responsive, self-oscillating gels that undergo biomimetic communication

Chemo-responsive, self-oscillating gels that undergo biomimetic communication

Amplitude and phase dynamics in oscillators with distributed-delay coupling

Self‐Organized Stationary Patterns in Networks of Bistable Chemical Reactions

Contact Info

Product

Resources

About