The Symmetry Perspective

Golubitsky, Martin; Stewart, Ian

doi:10.1007/978-3-0348-8167-8

Cited by 348 publications

(296 citation statements)

References 138 publications

(266 reference statements)

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“…In many cases the simplified model gives a good reproduction of experimental results, as in those discussed by Golubitsky and Stewart [9,Chapter 5]. There are situations, however, when not all experimentally observed patterns may be obtained from this analysis, as indicated by Gomes [10] who proposes that some of these patterns may arise as the projection of a three-dimensional periodic structure.…”

Section: 1mentioning

confidence: 80%

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On the projection of functions invariant under the action of a crystallographic group

Pinho

Labouriau

2014

Journal of Pure and Applied Algebra

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Abstract. We study functions defined in (n + 1)-dimensional domains that are invariant under the action of a crystallographic group. We give a complete description of the symmetries that remain after projection into an ndimensional subspace and compare it to similar results for the restriction to a subspace. We use the Fourier expansion of invariant functions and the action of the crystallographic group on the space of Fourier coefficients. Intermediate results relate symmetry groups to the dual of the lattice of periods.

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Section: 1mentioning

confidence: 80%

“…Knowledge of the symmetries is thus an essential step in dealing with this problem. For a more detailed treatment we refer the reader to [9,Chapter 5] and [11] where the 2-dimensional case is discussed, to [7] and, for issues arising from a projection, to [10].…”

Section: 1mentioning

confidence: 99%

On the projection of functions invariant under the action of a crystallographic group

Pinho

Labouriau

2014

Journal of Pure and Applied Algebra

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“…Another validation of this abstract level of analysis came recently from the study of the movements of three people in a sport context, showing interacting dynamics well predicted by group theoretic arguments (Yokoyama and Yamamoto, 2011). More generally, those challenging current directions demonstrate again that climbing up the abstractness tree is not the ethereal grail of some remote scientist, but is practically useful, as it enables to model and predict natural processes despite an incomplete knowledge of various underlying components of the processes studied (Golubitsky and Stewart, 2006). …”

Section: The Case For Topological Equivalencementioning

confidence: 99%

“…Here symmetric have to be understood as referring to the structure and intrinsic dynamics of the components, not the behavior. Symmetry between the intrinsic dynamics and the couplings of two individuals will give rise to synchronization, and possibly out of phase synchronization by half a period shift (Golubitsky and Stewart, 2006). However departure from symmetry can to some extent give also rise to behavioral synchronization.…”

Section: Further Outstanding Challengesmentioning

confidence: 99%

Challenges for the understanding of the dynamics of social coordination

Lagarde

2013

Front. Neurorobot.

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The way people interact can be examined by looking at the way they move relative to each other. Seeking the principles behind those interactions have consequences potentially related to any type of interpersonal function, far beyond the so-called “motor” processes typically associated with the study of movements, be it perceptive, cognitive, affective, pragmatic, or epistemic. Here, we present the way the framework of coordination dynamics define and addresses the interactive actions in a dyad. We first introduce the basics of pattern formation as the roots of the theoretical approach of coordination dynamics, and then the way this framework may contribute to establish a solution to classify behaviors. Thereafter we review promising empirical results on the dynamics of interpersonal coordination, and finally discuss were to go next to decipher the way the coordination between two people and the way each individual contribute may be disentangled.

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“…Thus, this system can be regarded as an assemble of nonlinear oscillators coupled by the tube structure. We have constructed two-oscillator systems and three-, four-, five-oscillator systems in rings by a cell patterning method and have shown that the symmetrically arranged oscillator-systems exhibit multiple oscillation patterns predicted by the symmetric Hopf bifurcation theory using geometrical symmetry proposed by Golubitsky and Stewart [1][2][3][4]. In order to obtain more information on the system, we investigated the responses to environmental change.…”

Section: Introductionmentioning

confidence: 99%

Control of Oscillation Patterns in a Symmetric Coupled Biological Oscillator System

Takamatsu

Tanaka

Yamamoto

et al. 2003

AIP Conference Proceedings

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Abstract. A chain of three-oscillator system was constructed with living biological oscillators of phasmodial slime mold, Physarum polycehalum and the oscillation patterns were analyzed by the symmetric Hopf bifurcation theory using group theory. Multi-stability of oscillation patterns was observed, even when the coupling strength was fixed. This suggests that the coupling strength is not an effective parameter to obtain a desired oscillation pattern among the multiple patterns. Here we propose a method to control oscillation patterns using resonance to external stimulus and demonstrate pattern switching induced by frequency resonance given to only one of oscillators in the system.

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The Symmetry Perspective

Cited by 348 publications

References 138 publications

On the projection of functions invariant under the action of a crystallographic group

On the projection of functions invariant under the action of a crystallographic group

Challenges for the understanding of the dynamics of social coordination

Control of Oscillation Patterns in a Symmetric Coupled Biological Oscillator System

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