Meta-dynamical adaptive systems and their applications to a fractal algorithm and a biological model
In this article, one defines two models of adaptive systems: the meta- dynamical adaptive system using the notion of Kalman dynamical systems and the adaptive differential equations using the notion of variable dimension spaces. This concept of variable dimension spaces relates the notion of spaces...
Saved in:
| Published in: | Physica. D Vol. 207; no. 1; pp. 79 - 90 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Amsterdam
Elsevier B.V
15.07.2005
Elsevier |
| Subjects: | |
| ISSN: | 0167-2789, 1872-8022 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | In this article, one defines two models of adaptive systems: the
meta-
dynamical adaptive system using the notion of Kalman dynamical systems and the
adaptive differential equations using the notion of
variable dimension spaces. This concept of variable dimension spaces relates the notion of spaces to the notion of dimensions. First, a computational model of the Douady’s Rabbit fractal is obtained by using the meta-dynamical adaptive system concept. Then, we focus on a defense-attack biological model described by our two formalisms. |
|---|---|
| AbstractList | In this article, one defines two models of adaptive systems: the
meta-
dynamical adaptive system using the notion of Kalman dynamical systems and the
adaptive differential equations using the notion of
variable dimension spaces. This concept of variable dimension spaces relates the notion of spaces to the notion of dimensions. First, a computational model of the Douady’s Rabbit fractal is obtained by using the meta-dynamical adaptive system concept. Then, we focus on a defense-attack biological model described by our two formalisms. In this article, one defines two models of adaptive systems: the meta-dynamical adaptive system using the notion of Kalman dynamical systems and the adaptive differential equations using the notion of variable dimension spaces. This concept of variable dimension spaces relates the notion of spaces to the notion of dimensions. First, a computational model of the Douady's Rabbit fractal is obtained by using the meta-dynamical adaptive system concept. Then, we focus on a defense-attack biological model described by our two formalisms. |
| Author | Moulay, Emmanuel Baguelin, Marc |
| Author_xml | – sequence: 1 givenname: Emmanuel surname: Moulay fullname: Moulay, Emmanuel email: emmanuel.moulay@ec-lille.fr organization: Laboratoire Paul Painlevé, UFR de Mathématiques Pures et Appliquées, Université de Sciences et Technologies de Lille, France – sequence: 2 givenname: Marc surname: Baguelin fullname: Baguelin, Marc email: mb556@cam.ac.uk organization: Department of Zoology, University of Cambridge, Downing Street, Cambridge CB2 3EJ, UK |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=16906791$$DView record in Pascal Francis https://hal.science/hal-00136495$$DView record in HAL |
| BookMark | eNqFkE1LxDAQhoMouH78Ai-5ePDQNUm3SXvwIOIXrHjRc5gmUzdL25QkLOy_t90VBQ8KAwPD8wwz7wk57H2PhFxwNueMy-v1fFhto50Lxor5VDw_IDNeKpGVTIhDMhsplQlVVsfkJMY1Y4yrXM2IfcEEmd320DkDLQULQ3IbpHEbE3aRQm9pWqELFIahHZnkfB9p8hRoE8CkSWo_fHBp1e1ooLXzrf_Y7eu8xfaMHDXQRjz_6qfk_eH-7e4pW74-Pt_dLjOTS5Uy4CCtWnChDBipuDGoKiyA15VopMlBFAXiooAaG1szXnAGC5BlbUpW1wLyU3K137uCVg_BdRC22oPTT7dLPc3Gr3O5qIoNH9nLPTtAHA8dX-mNi98WlxWTqpq4fM-Z4GMM2PwgTE_h67Xeha-n8PVUPB-t6pdlXNpFlwK49h_3Zu_iGNXGYdDROOwNWhfQJG29-9P_BNxRpNQ |
| CODEN | PDNPDT |
| CitedBy_id | crossref_primary_10_1016_j_cam_2006_03_036 crossref_primary_10_3390_e14101939 |
| Cites_doi | 10.1007/BF02591353 10.1112/jlms/s1-12.45.18 10.1002/cplx.10077 |
| ContentType | Journal Article |
| Copyright | 2005 Elsevier B.V. 2005 INIST-CNRS Distributed under a Creative Commons Attribution 4.0 International License |
| Copyright_xml | – notice: 2005 Elsevier B.V. – notice: 2005 INIST-CNRS – notice: Distributed under a Creative Commons Attribution 4.0 International License |
| DBID | AAYXX CITATION IQODW 1XC VOOES |
| DOI | 10.1016/j.physd.2005.05.013 |
| DatabaseName | CrossRef Pascal-Francis Hyper Article en Ligne (HAL) Hyper Article en Ligne (HAL) (Open Access) |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Physics |
| EISSN | 1872-8022 |
| EndPage | 90 |
| ExternalDocumentID | oai:HAL:hal-00136495v1 16906791 10_1016_j_physd_2005_05_013 S0167278905002149 |
| GroupedDBID | --K --M -~X .~1 0R~ 1B1 1RT 1~. 1~5 29O 4.4 457 4G. 5VS 7-5 71M 8P~ 9JN AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO ABAOU ABFNM ABMAC ABNEU ABXDB ABYKQ ACAZW ACDAQ ACFVG ACGFS ACNCT ACNNM ACRLP ADBBV ADEZE ADGUI ADIYS ADMUD AEBSH AEKER AFFNX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AIEXJ AIGVJ AIKHN AITUG AIVDX AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR ASPBG AVWKF AXJTR AZFZN BBWZM BKOJK BLXMC EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-Q GBLVA HMV HVGLF HZ~ H~9 IHE J1W K-O KOM M38 M41 MHUIS MO0 MVM N9A NDZJH O-L O9- OAUVE OGIMB OZT P-8 P-9 P2P PC. Q38 R2- RIG RNS ROL RPZ SDF SDG SDP SES SEW SPC SPCBC SPD SPG SSQ SSW SSZ T5K TN5 TWZ WUQ XJT XPP YNT YYP ~02 ~G- 9DU AATTM AAXKI AAYWO AAYXX ABWVN ACLOT ACRPL ADNMO ADVLN AEIPS AFJKZ AGQPQ AIIUN ANKPU APXCP CITATION EFKBS ~HD AFXIZ AGCQF AGRNS BNPGV IQODW SSH 1XC VOOES |
| ID | FETCH-LOGICAL-c367t-a1a6d74127cac671cce79e5a1b92f6c3a255ee45abefdb01510a4a68bc80bb2a3 |
| ISICitedReferencesCount | 2 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000230553100006&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0167-2789 |
| IngestDate | Tue Oct 28 08:50:57 EDT 2025 Mon Jul 21 09:16:03 EDT 2025 Sat Nov 29 03:57:23 EST 2025 Tue Nov 18 22:35:31 EST 2025 Fri Feb 23 02:16:03 EST 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Keywords | Adaptive systems 92D25 37F50 92D15 93A05 Biological systems Fractal algorithm Dynamical systems Non linear phenomenon 92D25 Dynamical systems Algorithms Fractal Differential equations Models dynamical systems biological systems fractal algorithm adaptive systems |
| Language | English |
| License | https://www.elsevier.com/tdm/userlicense/1.0 CC BY 4.0 Distributed under a Creative Commons Attribution 4.0 International License: http://creativecommons.org/licenses/by/4.0 |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c367t-a1a6d74127cac671cce79e5a1b92f6c3a255ee45abefdb01510a4a68bc80bb2a3 |
| ORCID | 0000-0001-8687-884X |
| OpenAccessLink | https://hal.science/hal-00136495 |
| PageCount | 12 |
| ParticipantIDs | hal_primary_oai_HAL_hal_00136495v1 pascalfrancis_primary_16906791 crossref_primary_10_1016_j_physd_2005_05_013 crossref_citationtrail_10_1016_j_physd_2005_05_013 elsevier_sciencedirect_doi_10_1016_j_physd_2005_05_013 |
| PublicationCentury | 2000 |
| PublicationDate | 2005-07-15 |
| PublicationDateYYYYMMDD | 2005-07-15 |
| PublicationDate_xml | – month: 07 year: 2005 text: 2005-07-15 day: 15 |
| PublicationDecade | 2000 |
| PublicationPlace | Amsterdam |
| PublicationPlace_xml | – name: Amsterdam |
| PublicationTitle | Physica. D |
| PublicationYear | 2005 |
| Publisher | Elsevier B.V Elsevier |
| Publisher_xml | – name: Elsevier B.V – name: Elsevier |
| References | Mandelbrot (bib5) 1982 Tricot (bib20) 1993 Alexander (bib12) 1994 Besicovitch, Ursell (bib17) 1937; 12 Baguelin, Lefèvre, Richard (bib22) 2002 Zeigler, Praehofer, Kim (bib11) 2000 Jen (bib10) 2003; 8 Mandelbrot (bib6) 1980 Baguelin, Lefèvre, Richard (bib8) 2003 Hurewicz, Wallman (bib19) 1941 Holland (bib4) 1992 Tricot (bib18) 1981; 293 Peitgen, Saupe (bib15) 1988 R.E. Kalman, P.L. Falb, M.A. Arbib, Topics in Mathematical System Theory, International Series in Pure and Applied Mathematics, McGraw-Hill, 1969. A. Douady, J.H. Hubbard, Etude dynamique des polynômes complexes, (première et deuxième partie), Publications Mathématiques d’Orsay 84–02, 85–04. Gell-Mann (bib2) 1994 Rosen (bib3) 1985 M. Baguelin, Modélisation de systèmes complexes par métadynamiques: Application à la modélisation de populations en coévolution, Ph.D. thesis, Université des sciences et technologie de Lille, 2003. Brolin (bib13) 1965; 6 J. Peyrière, Calculs de dimension de hausdorff, Analyse Harmonique d’Orsay, p. 188. Mosekilde, Strandorf, Thomsen, Baier (bib21) 1996 Waldrop (bib1) 1992 Mandelbrot (10.1016/j.physd.2005.05.013_bib5) 1982 Jen (10.1016/j.physd.2005.05.013_bib10) 2003; 8 Hurewicz (10.1016/j.physd.2005.05.013_bib19) 1941 Holland (10.1016/j.physd.2005.05.013_bib4) 1992 Baguelin (10.1016/j.physd.2005.05.013_bib22) 2002 Mandelbrot (10.1016/j.physd.2005.05.013_bib6) 1980 Mosekilde (10.1016/j.physd.2005.05.013_bib21) 1996 Zeigler (10.1016/j.physd.2005.05.013_bib11) 2000 Alexander (10.1016/j.physd.2005.05.013_bib12) 1994 Tricot (10.1016/j.physd.2005.05.013_bib18) 1981; 293 Waldrop (10.1016/j.physd.2005.05.013_bib1) 1992 10.1016/j.physd.2005.05.013_bib14 Brolin (10.1016/j.physd.2005.05.013_bib13) 1965; 6 10.1016/j.physd.2005.05.013_bib7 10.1016/j.physd.2005.05.013_bib16 Tricot (10.1016/j.physd.2005.05.013_bib20) 1993 Gell-Mann (10.1016/j.physd.2005.05.013_bib2) 1994 Rosen (10.1016/j.physd.2005.05.013_bib3) 1985 Peitgen (10.1016/j.physd.2005.05.013_bib15) 1988 Baguelin (10.1016/j.physd.2005.05.013_bib8) 2003 Besicovitch (10.1016/j.physd.2005.05.013_bib17) 1937; 12 10.1016/j.physd.2005.05.013_bib9 |
| References_xml | – reference: J. Peyrière, Calculs de dimension de hausdorff, Analyse Harmonique d’Orsay, p. 188. – volume: 293 start-page: 549 year: 1981 end-page: 552 ident: bib18 article-title: Douze définitions de la densité logarithmique publication-title: C. R. Académie des Sciences, Paris, Série I Math – year: 1982 ident: bib5 article-title: Des Monstres de Cantor et de Peano à la Géométrie Fractale de la Nature – volume: 6 start-page: 103 year: 1965 end-page: 144 ident: bib13 article-title: Invariant sets under iteration of rational functions publication-title: Arkiv for Matematik – year: 2000 ident: bib11 article-title: Theory of Modelling and Simulation: Integrating Discrete Event and Continuous Complex Dynamic Systems – year: 2003 ident: bib8 article-title: A formalism for models with a metadynamically varying structure publication-title: Proceedings of the IEEE European Control Conference – start-page: 466 year: 2002 end-page: 471 ident: bib22 article-title: Preliminary approach to the simulation of coevolution in an ecosystem publication-title: Proceedings of the 16th European Simulation Multiconference – volume: 8 start-page: 12 year: 2003 end-page: 18 ident: bib10 article-title: Stable or robust? What’s the difference? publication-title: Complexity – year: 1988 ident: bib15 article-title: The Science of Fractal Images – year: 1941 ident: bib19 article-title: Dimension Theory – reference: A. Douady, J.H. Hubbard, Etude dynamique des polynômes complexes, (première et deuxième partie), Publications Mathématiques d’Orsay 84–02, 85–04. – year: 1992 ident: bib4 article-title: Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence – year: 1992 ident: bib1 article-title: Complexity: The Emerging Science at the Edge of Chaos – reference: M. Baguelin, Modélisation de systèmes complexes par métadynamiques: Application à la modélisation de populations en coévolution, Ph.D. thesis, Université des sciences et technologie de Lille, 2003. – year: 1993 ident: bib20 article-title: Courbes et Dimension Fractale – reference: R.E. Kalman, P.L. Falb, M.A. Arbib, Topics in Mathematical System Theory, International Series in Pure and Applied Mathematics, McGraw-Hill, 1969. – year: 1996 ident: bib21 article-title: Topics in Nonlinear Dynamics – year: 1994 ident: bib2 article-title: The Quark and the Jaguar: Adventures in the Simple and the Complex – year: 1985 ident: bib3 article-title: Theoretical Biology and Complexity: Three Essays on the Natural Philosophy of Complex Systems – year: 1980 ident: bib6 article-title: Les Objets Fractals – volume: 12 start-page: 18 year: 1937 end-page: 25 ident: bib17 article-title: Sets of fractional dimensions (v): on dimensional numbers of some continuous curves publication-title: J. Lond. Math. Soc. – year: 1994 ident: bib12 article-title: A History of Complex Dynamics: From Schrüder to Fatou and Julia – ident: 10.1016/j.physd.2005.05.013_bib7 – year: 1996 ident: 10.1016/j.physd.2005.05.013_bib21 – year: 1994 ident: 10.1016/j.physd.2005.05.013_bib12 – volume: 6 start-page: 103 year: 1965 ident: 10.1016/j.physd.2005.05.013_bib13 article-title: Invariant sets under iteration of rational functions publication-title: Arkiv for Matematik doi: 10.1007/BF02591353 – year: 1992 ident: 10.1016/j.physd.2005.05.013_bib4 – ident: 10.1016/j.physd.2005.05.013_bib9 – year: 1994 ident: 10.1016/j.physd.2005.05.013_bib2 – year: 1982 ident: 10.1016/j.physd.2005.05.013_bib5 – year: 1980 ident: 10.1016/j.physd.2005.05.013_bib6 – start-page: 466 year: 2002 ident: 10.1016/j.physd.2005.05.013_bib22 article-title: Preliminary approach to the simulation of coevolution in an ecosystem – year: 1941 ident: 10.1016/j.physd.2005.05.013_bib19 – year: 1992 ident: 10.1016/j.physd.2005.05.013_bib1 – year: 1988 ident: 10.1016/j.physd.2005.05.013_bib15 – year: 1993 ident: 10.1016/j.physd.2005.05.013_bib20 – year: 1985 ident: 10.1016/j.physd.2005.05.013_bib3 – ident: 10.1016/j.physd.2005.05.013_bib16 – ident: 10.1016/j.physd.2005.05.013_bib14 – volume: 293 start-page: 549 year: 1981 ident: 10.1016/j.physd.2005.05.013_bib18 article-title: Douze définitions de la densité logarithmique publication-title: C. R. Académie des Sciences, Paris, Série I Math – volume: 12 start-page: 18 issue: 45 year: 1937 ident: 10.1016/j.physd.2005.05.013_bib17 article-title: Sets of fractional dimensions (v): on dimensional numbers of some continuous curves publication-title: J. Lond. Math. Soc. doi: 10.1112/jlms/s1-12.45.18 – volume: 8 start-page: 12 issue: 3 year: 2003 ident: 10.1016/j.physd.2005.05.013_bib10 article-title: Stable or robust? What’s the difference? publication-title: Complexity doi: 10.1002/cplx.10077 – year: 2003 ident: 10.1016/j.physd.2005.05.013_bib8 article-title: A formalism for models with a metadynamically varying structure – year: 2000 ident: 10.1016/j.physd.2005.05.013_bib11 |
| SSID | ssj0001737 |
| Score | 1.7799164 |
| Snippet | In this article, one defines two models of adaptive systems: the
meta-
dynamical adaptive system using the notion of Kalman dynamical systems and the
adaptive... In this article, one defines two models of adaptive systems: the meta-dynamical adaptive system using the notion of Kalman dynamical systems and the adaptive... |
| SourceID | hal pascalfrancis crossref elsevier |
| SourceType | Open Access Repository Index Database Enrichment Source Publisher |
| StartPage | 79 |
| SubjectTerms | Adaptation and Self-Organizing Systems Adaptive systems Biological systems Chaotic Dynamics Dynamical systems Exact sciences and technology Fractal algorithm Nonlinear Sciences Physics |
| Title | Meta-dynamical adaptive systems and their applications to a fractal algorithm and a biological model |
| URI | https://dx.doi.org/10.1016/j.physd.2005.05.013 https://hal.science/hal-00136495 |
| Volume | 207 |
| WOSCitedRecordID | wos000230553100006&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1872-8022 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001737 issn: 0167-2789 databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3_a9NAFD_cpuAQ0alYv4xD_K1m5JJeLvdjlcqUdQyc0t_Cuy_ZOrq0NOnYn7_7kqQpxaGCUEI5klyazyfvXl7f-zyEPirCwkhDYh-kMBhwQgMhQxbksdAKNKe5ky_-dcJOT9PJhJ_VoezStRNgRZHe3vLFf4XajBmwbensX8DdntQMmO8GdLM1sJvtHwE_1hUEyjeat0IAChYuPchrNpdNyuR02e_-eW19UOjntmbKHjS7mC-n1aXvnwF9L9Xkzuda53Rd2jOP9NE6d3g8X83AgTe6voZipdssjs9wsdJ1i_ixue8bMQdqg5m-6tIHwraKYXxs0thcW1jrlxZvT1NmDG4YbRjcyPe53WCWN5-MdxZi30Z0y8T7aMPVkY38qDooZqVX4_WK1uYZ_rDX5Gp9qROH4ztoL2KUG_O3N_w2mnxvF23CvLxq8xsagSqXCrg11e-cmJ1Lm037ZAGlAST3nVE67sr5M_S0fs_AQ8-P5-iBLg7Qfkd98gA98siVL5Da5AxuOINrzmDDAuw4g7ucwdUcA645g1vOuL0BrzmDHWdeop9fR-dfjoO6_UYg44RVARBIlHE4IyZBJoxIqRnXFIjgUZ7IGMzbqNYDCkLnShi3koQwgCQVMg2FiCB-hXaLeaFfIxzLWFsIiBJ0oAwOeRIJQVMVEh2livdQ1NzPTNba9LZFyixrkhCvMgeC7ZpKM_shcQ99ag9aeGmW-3dPGqCy2rv0XmNmmHX_gR8MrO0UVo_9eHiS2TGneDjg9Ib00OEG6usrskrgjJM3_zr9W_R4_Qi-Q7vVcqXfo4fyppqWy8Oax3eSTrgu |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Meta-dynamical+adaptive+systems+and+their+applications+to+a+fractal+algorithm+and+a+biological+model&rft.jtitle=Physica.+D&rft.au=Moulay%2C+Emmanuel&rft.au=Baguelin%2C+Marc&rft.date=2005-07-15&rft.pub=Elsevier+B.V&rft.issn=0167-2789&rft.eissn=1872-8022&rft.volume=207&rft.issue=1&rft.spage=79&rft.epage=90&rft_id=info:doi/10.1016%2Fj.physd.2005.05.013&rft.externalDocID=S0167278905002149 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0167-2789&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0167-2789&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0167-2789&client=summon |