Algorithms for concatenating templates

Gilmore, Robert; Rosalie, Martin

doi:10.1063/1.4942799

Cited by 3 publications

(6 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is a figure that represents the topological structure of a chaotic attractor. Since the 1990s there have been two different ways to represent templates with linking matrices that are still used today, as one can see in the recent paper of Gilmore and Rosalie [12], where algorithms are given to switch from one representation to the other. Hereinafter, the representation first given by Melvin and Tufillaro [17] is considered.…”

Section: Conventionmentioning

confidence: 99%

Visualizing the Template of a Chaotic Attractor

Olszewski¹,

Meder²,

Kieffer³

et al. 2018

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

0000−0001−9926−058X] , Jeff Meder 1[0000−0002−2360−8487] , Emmanuel Kieffer 2[0000−0002−5530−8577] , Raphaël Bleuse 1[0000−0002−6728−2132] , Martin Rosalie 2[0000−0003−3676−120X] , Grégoire Danoy 1[0000−0001−9419−4210] , and Pascal Bouvry 1,2[0000−0001−9338−2834]Abstract. Chaotic attractors are solutions of deterministic processes, of which the topology can be described by templates. We consider templates of chaotic attractors bounded by a genus-1 torus described by a linking matrix. This article introduces a novel and unique tool to validate a linking matrix, to optimize the compactness of the corresponding template and to draw this template. The article provides a detailed description of the different validation steps and the extraction of an order of crossings from the linking matrix leading to a template of minimal height. Finally, the drawing process of the template corresponding to the matrix is saved in a Scalable Vector Graphics (SVG) file.

show abstract

Section: Conventionmentioning

confidence: 99%

Visualizing the Template of a Chaotic Attractor

Olszewski¹,

Meder²,

Kieffer³

et al. 2018

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

show abstract

“…A mixer M is defined by a linking matrix M where the right side is " " to represent the merging at the branch line with respect to the Tufillaro convention [8] (see [7] to distinguish the two linking matrix representation conventions). For the following section, we named linkers and mixers of template as actions and also consider torsions and permutations are linkers.…”

Section: Algebraic Relation Between Linking Matrixmentioning

confidence: 99%

“…Theorem 1 [7] Given a template T containing a mixer A of n a strips defined by the linking matrix A and a mixer B of n b strips defined by the linking matrix B. If A is concatenated before B, then A ⊕ B ≡ C, where C is a mixer of n a × n b strips defined by the linking matrix C that is the sum of the expanded linking matrices A and B with additional permutations due to the insertion of A…”

Section: Concatenation Of Mixersmentioning

confidence: 99%

“…Some algebraic relations are introduced to perform operations between the linking matrix. Gilmore et al propose the concatenation of linking matrix [3] and we recently propose algorithms to perform this concatenation [7]. Tufillaro and co-workers [8,9] propose another algebraic representation of a linking matrix: only a matrix satisfying the orientation convention to know how strips are ordered.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Chaotic mechanism description by an elementary mixer for the template of an attractor

Rosalie

2017

Preprint

Self Cite

View full text Add to dashboard Cite

Templates can be used to describe the topological properties of chaotic attractors. For attractors bounded by genus one torus, these templates are described by a linking matrix. For a given attractor, it has been shown that the template depends on the Poincaré section chosen to performed the analysis. The purpose of this article is to present an algorithm that gives the elementary mixer of a template in order to have a unique way to describe a chaotic mechanism. This chaotic mechanism is described with a linking matrix and we also provide a method to generate and classify all the possible chaotic mechanisms made of two to five strips.

show abstract

“…conventions, see [19]. Here, the double line in the right bracket refers to the standard insertion convention indicating that the squeezing mechanism is included in the linking matrix.…”

Section: (Vi) Compute Numerically the Linking Numbers;mentioning

confidence: 99%

Templates and subtemplates of Rössler attractors from a bifurcation diagram

Rosalie¹

2016

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

We study the bifurcation diagram of the Rössler system. It displays the various dynamical regimes of the system (stable or chaotic) when a parameter is varied. We choose a diagram that exhibits coexisting attractors and banded chaos. We use the topological characterization method to study these attractors. Then, we details how the templates of these attractors are subtemplates of a unique template. Our main result is that only one template describe the topological structure of height attractors. This leads to a topological partition of the bifurcation diagram that gives the symbolic dynamic of all bifurcation diagram attractors with a unique template.

show abstract

Algorithms for concatenating templates

Cited by 3 publications

References 18 publications

Visualizing the Template of a Chaotic Attractor

Visualizing the Template of a Chaotic Attractor

Chaotic mechanism description by an elementary mixer for the template of an attractor

Templates and subtemplates of Rössler attractors from a bifurcation diagram

Contact Info

Product

Resources

About