Chemical Turbulence

Kuramoto, Yoshio

doi:10.1007/978-3-642-69689-3_7

Cited by 223 publications

(340 citation statements)

References 0 publications

Supporting

Mentioning

339

Contrasting

Order By: Relevance

“…These patterns are "building blocks" of wave patterns like target patterns, wave segments, and spiral waves in two as well as scroll waves in three spatial dimensions, respectively. Another important class of RD patterns are stationary, breathing, and moving localized spots [1][2][3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Analytical, Optimal, and Sparse Optimal Control of Traveling Wave Solutions to Reaction-Diffusion Systems

Ryll

Löber

Martens

et al. 2016

Understanding Complex Systems

View full text Add to dashboard Cite

Abstract. This work deals with the position control of selected patterns in reactiondiffusion systems. Exemplarily, the Schlögl and FitzHugh-Nagumo model are discussed using three different approaches. First, an analytical solution is proposed. Second, the standard optimal control procedure is applied. The third approach extends standard optimal control to so-called sparse optimal control that results in very localized control signals and allows the analysis of second order optimality conditions.

show abstract

Section: Introductionmentioning

confidence: 99%

Analytical, Optimal, and Sparse Optimal Control of Traveling Wave Solutions to Reaction-Diffusion Systems

Ryll

Löber

Martens

et al. 2016

Understanding Complex Systems

View full text Add to dashboard Cite

show abstract

“…In order to avoid an ad-hoc toy model, we propose a broad class of models from which we derive a simple model by means of centre-manifold reduction and phase reduction (19).…”

mentioning

confidence: 99%

General Chemotactic Model of Oscillators

2007

View full text Add to dashboard Cite

Nonlinear coupling between inter-and intra-element dynamics appears as a collective behaviour of elements. The elements in this paper denote symptoms such as a bacterium having an internal network of genes and proteins, a reactive droplet, a neuron in networks, etc. In order to elucidate the capability of such systems, a simple and reasonable model is derived. This model exhibits the rich patterns of systems such as cell membrane, cell fusion, cell growing, cell division, firework, branch, and clustered clusters (self-organized hierarchical structure, modular network). This model is extremely simple yet powerful; therefore, it is expected to impact several disciplines. * Electronic address: dan@ton.scphys.kyoto-u.ac.jp 1

show abstract

“…One of the most successful attempts to understand synchronization phenomena was due to Kuramoto [20], who analyzed a model of phase oscillators coupled through the sine of their phase differences. The model is rich enough to display a large variety of synchronization patterns and sufficiently flexible to be adapted to many different contexts [22].…”

Section: Synchronization: Kuramoto's Modelmentioning

confidence: 99%

“…In a completely different scenario, physicists have largely studied the dynamics of complex biological systems, and in particular the paradigmatic analysis of large populations of coupled oscillators [18,19,20]. The connection between the study of synchronization processes and complex networks is interesting by itself.…”

Section: Introductionmentioning

confidence: 99%

Synchronization processes in complex networks

Arenas

Dı́az-Guilera

Pérez-Vicente

2006

Physica D: Nonlinear Phenomena

143

View full text Add to dashboard Cite

We present an extended analysis, based on the dynamics towards synchronization of a system of coupled oscillators, of the hierarchy of communities in complex networks. In the synchronization process, different structures corresponding to well defined communities of nodes appear in a hierarchical way. The analysis also provides a useful connection between synchronization dynamics, complex networks topology and spectral graph analysis.

show abstract

Chemical Turbulence

Cited by 223 publications

References 0 publications

Analytical, Optimal, and Sparse Optimal Control of Traveling Wave Solutions to Reaction-Diffusion Systems

Analytical, Optimal, and Sparse Optimal Control of Traveling Wave Solutions to Reaction-Diffusion Systems

General Chemotactic Model of Oscillators

Synchronization processes in complex networks

Contact Info

Product

Resources

About