Reconstruction of systems with delayed feedback: I. Theory View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2000-04

AUTHORS

M.J. Bünner, M. Ciofini, A. Giaquinta, R. Hegger, H. Kantz, R. Meucci, A. Politi

ABSTRACT

High-dimensional chaos displayed by multi-component systems with a single time-delayed feedback is shown to be accessible to time series analysis of a scalar variable only. The mapping of the original dynamics onto scalar time-delay systems defined on sufficiently high dimensional spaces is thoroughly discussed. The dimension of the “embedding” space turns out to be independent of the delay time and thus of the dimensionality of the attractor dynamics. As a consequence, the procedure described in the present paper turns out to be definitely advantageous with respect to the standard embedding technique in the case of high-dimensional chaos, when the latter is practically unapplicable. The mapping is not exact when delayed maps are used to reproduce the dynamics of time-continuous systems, but the errors can be kept under control. In this context, the approximation of delay-differential equations is discussed with reference to different classes of maps. Appropriate tools to estimate the a priori unknown delay time and the number of hidden components are introduced. The generalized Mackey-Glass system is investigated in detail as a testing ground for the theoretical considerations. More... »

PAGES

165-176

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s100530050538

DOI

http://dx.doi.org/10.1007/s100530050538

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1054520946


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0102", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Applied Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Istituto Nazionale di Ottica", 
          "id": "https://www.grid.ac/institutes/grid.425378.f", 
          "name": [
            "Istituto Nazionale di Ottica Applicata, Largo E. Fermi 6, 50125 Firenze, Italy, IT"
          ], 
          "type": "Organization"
        }, 
        "familyName": "B\u00fcnner", 
        "givenName": "M.J.", 
        "id": "sg:person.012457663605.18", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012457663605.18"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Istituto Nazionale di Ottica", 
          "id": "https://www.grid.ac/institutes/grid.425378.f", 
          "name": [
            "Istituto Nazionale di Ottica Applicata, Largo E. Fermi 6, 50125 Firenze, Italy, IT"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Ciofini", 
        "givenName": "M.", 
        "id": "sg:person.011012362517.51", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011012362517.51"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "name": [
            "Instituto Pluridisciplinar, Paseo Juan XXIII 1, 28040 Madrid, Spain, ES"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Giaquinta", 
        "givenName": "A.", 
        "id": "sg:person.012066633647.36", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012066633647.36"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Max Planck Institute for the Physics of Complex Systems", 
          "id": "https://www.grid.ac/institutes/grid.419560.f", 
          "name": [
            "Max-Planck-Institut f\u00fcr Physik komplexer Systeme, N\u00f6thnitzer Str. 38, 01187 Dresden, Germany, DE"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Hegger", 
        "givenName": "R.", 
        "id": "sg:person.01014737157.98", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01014737157.98"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Max Planck Institute for the Physics of Complex Systems", 
          "id": "https://www.grid.ac/institutes/grid.419560.f", 
          "name": [
            "Max-Planck-Institut f\u00fcr Physik komplexer Systeme, N\u00f6thnitzer Str. 38, 01187 Dresden, Germany, DE"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Kantz", 
        "givenName": "H.", 
        "id": "sg:person.0671621336.20", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0671621336.20"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Istituto Nazionale di Ottica", 
          "id": "https://www.grid.ac/institutes/grid.425378.f", 
          "name": [
            "Istituto Nazionale di Ottica Applicata, Largo E. Fermi 6, 50125 Firenze, Italy, IT"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Meucci", 
        "givenName": "R.", 
        "id": "sg:person.01233555630.53", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01233555630.53"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Istituto Nazionale di Ottica", 
          "id": "https://www.grid.ac/institutes/grid.425378.f", 
          "name": [
            "Istituto Nazionale di Ottica Applicata, Largo E. Fermi 6, 50125 Firenze, Italy, IT"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Politi", 
        "givenName": "A.", 
        "id": "sg:person.013264105675.78", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013264105675.78"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "2000-04", 
    "datePublishedReg": "2000-04-01", 
    "description": "High-dimensional chaos displayed by multi-component systems with a single time-delayed feedback is shown to be accessible to time series analysis of a scalar variable only. The mapping of the original dynamics onto scalar time-delay systems defined on sufficiently high dimensional spaces is thoroughly discussed. The dimension of the \u201cembedding\u201d space turns out to be independent of the delay time and thus of the dimensionality of the attractor dynamics. As a consequence, the procedure described in the present paper turns out to be definitely advantageous with respect to the standard embedding technique in the case of high-dimensional chaos, when the latter is practically unapplicable. The mapping is not exact when delayed maps are used to reproduce the dynamics of time-continuous systems, but the errors can be kept under control. In this context, the approximation of delay-differential equations is discussed with reference to different classes of maps. Appropriate tools to estimate the a priori unknown delay time and the number of hidden components are introduced. The generalized Mackey-Glass system is investigated in detail as a testing ground for the theoretical considerations.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s100530050538", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1295077", 
        "issn": [
          "1434-6060", 
          "1434-6079"
        ], 
        "name": "The European Physical Journal D", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "2", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "10"
      }
    ], 
    "name": "Reconstruction of systems with delayed feedback: I. Theory", 
    "pagination": "165-176", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "9253775f843caa913d826bd281831436334d436ce1c96306677e258ad9505640"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s100530050538"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1054520946"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s100530050538", 
      "https://app.dimensions.ai/details/publication/pub.1054520946"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-10T14:02", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8660_00000483.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007/s100530050538"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s100530050538'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s100530050538'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s100530050538'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s100530050538'


 

This table displays all metadata directly associated to this object as RDF triples.

108 TRIPLES      20 PREDICATES      27 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s100530050538 schema:about anzsrc-for:01
2 anzsrc-for:0102
3 schema:author Nfd1dd53ca5414d6a9b297c78e5577a8a
4 schema:datePublished 2000-04
5 schema:datePublishedReg 2000-04-01
6 schema:description High-dimensional chaos displayed by multi-component systems with a single time-delayed feedback is shown to be accessible to time series analysis of a scalar variable only. The mapping of the original dynamics onto scalar time-delay systems defined on sufficiently high dimensional spaces is thoroughly discussed. The dimension of the “embedding” space turns out to be independent of the delay time and thus of the dimensionality of the attractor dynamics. As a consequence, the procedure described in the present paper turns out to be definitely advantageous with respect to the standard embedding technique in the case of high-dimensional chaos, when the latter is practically unapplicable. The mapping is not exact when delayed maps are used to reproduce the dynamics of time-continuous systems, but the errors can be kept under control. In this context, the approximation of delay-differential equations is discussed with reference to different classes of maps. Appropriate tools to estimate the a priori unknown delay time and the number of hidden components are introduced. The generalized Mackey-Glass system is investigated in detail as a testing ground for the theoretical considerations.
7 schema:genre research_article
8 schema:inLanguage en
9 schema:isAccessibleForFree false
10 schema:isPartOf Nc158d910b2ef4978a6a2a2e101446664
11 Nd73c01db8caa4bb2a15dd415d3e02886
12 sg:journal.1295077
13 schema:name Reconstruction of systems with delayed feedback: I. Theory
14 schema:pagination 165-176
15 schema:productId N9b903ab9173749e39ce83c1bb6f4afb5
16 Na2ab43a9832041339cd6c9b345ce1b80
17 Nd85e4219178f4f27a40e3da2056a3889
18 schema:sameAs https://app.dimensions.ai/details/publication/pub.1054520946
19 https://doi.org/10.1007/s100530050538
20 schema:sdDatePublished 2019-04-10T14:02
21 schema:sdLicense https://scigraph.springernature.com/explorer/license/
22 schema:sdPublisher N773deb76db3b4cda9ce16c6c821b8ea0
23 schema:url http://link.springer.com/10.1007/s100530050538
24 sgo:license sg:explorer/license/
25 sgo:sdDataset articles
26 rdf:type schema:ScholarlyArticle
27 N06fdd50685954409b9c4efdb89c47cff rdf:first sg:person.01014737157.98
28 rdf:rest N48d2a78c816f452aa839ba7364449930
29 N469b1dbd5bf1483f89ffc6931fde94dd rdf:first sg:person.013264105675.78
30 rdf:rest rdf:nil
31 N48d2a78c816f452aa839ba7364449930 rdf:first sg:person.0671621336.20
32 rdf:rest Nfb238e82e27f4082b60a0832dd07aa10
33 N5a6a0d447a1b4a8f9da82eed6f900627 schema:name Instituto Pluridisciplinar, Paseo Juan XXIII 1, 28040 Madrid, Spain, ES
34 rdf:type schema:Organization
35 N773deb76db3b4cda9ce16c6c821b8ea0 schema:name Springer Nature - SN SciGraph project
36 rdf:type schema:Organization
37 N9b903ab9173749e39ce83c1bb6f4afb5 schema:name doi
38 schema:value 10.1007/s100530050538
39 rdf:type schema:PropertyValue
40 Na2ab43a9832041339cd6c9b345ce1b80 schema:name readcube_id
41 schema:value 9253775f843caa913d826bd281831436334d436ce1c96306677e258ad9505640
42 rdf:type schema:PropertyValue
43 Nc158d910b2ef4978a6a2a2e101446664 schema:issueNumber 2
44 rdf:type schema:PublicationIssue
45 Ncc6f7086e4684422bdfaf44580343afa rdf:first sg:person.011012362517.51
46 rdf:rest Nea6e9b6d1d7d4f80911da70ddc82772e
47 Nd73c01db8caa4bb2a15dd415d3e02886 schema:volumeNumber 10
48 rdf:type schema:PublicationVolume
49 Nd85e4219178f4f27a40e3da2056a3889 schema:name dimensions_id
50 schema:value pub.1054520946
51 rdf:type schema:PropertyValue
52 Nea6e9b6d1d7d4f80911da70ddc82772e rdf:first sg:person.012066633647.36
53 rdf:rest N06fdd50685954409b9c4efdb89c47cff
54 Nfb238e82e27f4082b60a0832dd07aa10 rdf:first sg:person.01233555630.53
55 rdf:rest N469b1dbd5bf1483f89ffc6931fde94dd
56 Nfd1dd53ca5414d6a9b297c78e5577a8a rdf:first sg:person.012457663605.18
57 rdf:rest Ncc6f7086e4684422bdfaf44580343afa
58 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
59 schema:name Mathematical Sciences
60 rdf:type schema:DefinedTerm
61 anzsrc-for:0102 schema:inDefinedTermSet anzsrc-for:
62 schema:name Applied Mathematics
63 rdf:type schema:DefinedTerm
64 sg:journal.1295077 schema:issn 1434-6060
65 1434-6079
66 schema:name The European Physical Journal D
67 rdf:type schema:Periodical
68 sg:person.01014737157.98 schema:affiliation https://www.grid.ac/institutes/grid.419560.f
69 schema:familyName Hegger
70 schema:givenName R.
71 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01014737157.98
72 rdf:type schema:Person
73 sg:person.011012362517.51 schema:affiliation https://www.grid.ac/institutes/grid.425378.f
74 schema:familyName Ciofini
75 schema:givenName M.
76 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011012362517.51
77 rdf:type schema:Person
78 sg:person.012066633647.36 schema:affiliation N5a6a0d447a1b4a8f9da82eed6f900627
79 schema:familyName Giaquinta
80 schema:givenName A.
81 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012066633647.36
82 rdf:type schema:Person
83 sg:person.01233555630.53 schema:affiliation https://www.grid.ac/institutes/grid.425378.f
84 schema:familyName Meucci
85 schema:givenName R.
86 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01233555630.53
87 rdf:type schema:Person
88 sg:person.012457663605.18 schema:affiliation https://www.grid.ac/institutes/grid.425378.f
89 schema:familyName Bünner
90 schema:givenName M.J.
91 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012457663605.18
92 rdf:type schema:Person
93 sg:person.013264105675.78 schema:affiliation https://www.grid.ac/institutes/grid.425378.f
94 schema:familyName Politi
95 schema:givenName A.
96 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013264105675.78
97 rdf:type schema:Person
98 sg:person.0671621336.20 schema:affiliation https://www.grid.ac/institutes/grid.419560.f
99 schema:familyName Kantz
100 schema:givenName H.
101 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0671621336.20
102 rdf:type schema:Person
103 https://www.grid.ac/institutes/grid.419560.f schema:alternateName Max Planck Institute for the Physics of Complex Systems
104 schema:name Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, 01187 Dresden, Germany, DE
105 rdf:type schema:Organization
106 https://www.grid.ac/institutes/grid.425378.f schema:alternateName Istituto Nazionale di Ottica
107 schema:name Istituto Nazionale di Ottica Applicata, Largo E. Fermi 6, 50125 Firenze, Italy, IT
108 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...