Spatially inhomogeneous modes of logistic differential equation with delay and small diffusion in a flat area View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2017-09

AUTHORS

S. Glyzin, V. Goryunov, A. Kolesov

ABSTRACT

In the paper we consider the problem of searching for coexisting modes in a nonlinear boundary value problem with a delay from population dynamics. For this we construct the asymptotic of spatially homogeneous cycle using the normal forms method and research the dependence of its stability on the diffusion parameter. Then we find coexisting attractors of the problem using numerical methods. Numerical experiment required an application of massively parallel computing systems and adaptation of solutions search algorithms to them. Based on the numerical analysis we come to the conclusion of the existence in the boundary value problem of solutions of two types. The first type has a simple spatial distribution and inherits the properties of a homogeneous solution. The second called the mode of self-organization is more complex distributed in space and is much more preferred in terms of population dynamics. More... »

PAGES

898-905

References to SciGraph publications

  • 1996. Theory and Applications of Partial Functional Differential Equations in NONE
  • 2013-12. Dimensional characteristics of diffusion chaos in AUTOMATIC CONTROL AND COMPUTER SCIENCES
  • 2004-12. Nonlocality of Reaction-Diffusion Equations Induced by Delay: Biological Modeling and Nonlinear Dynamics in JOURNAL OF MATHEMATICAL SCIENCES
  • 2010-05. Finite-dimensional models of diffusion chaos in COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS
  • 2013-12. Asymptotics of the solutions of the generalized Hutchinson equation in AUTOMATIC CONTROL AND COMPUTER SCIENCES
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1134/s1995080217050110

    DOI

    http://dx.doi.org/10.1134/s1995080217050110

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1091827339


    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/2008/0103", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Numerical and Computational 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": "Scientific Center", 
              "id": "https://www.grid.ac/institutes/grid.465407.4", 
              "name": [
                "Yaroslavl State University, 150000, Yaroslavl, Russia", 
                "Scientific Center in Chernogolovka of Russian Academy of Sciences, 142432, Chernogolovka, Moscow oblast, Russia"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Glyzin", 
            "givenName": "S.", 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Scientific Center", 
              "id": "https://www.grid.ac/institutes/grid.465407.4", 
              "name": [
                "Yaroslavl State University, 150000, Yaroslavl, Russia", 
                "Scientific Center in Chernogolovka of Russian Academy of Sciences, 142432, Chernogolovka, Moscow oblast, Russia"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Goryunov", 
            "givenName": "V.", 
            "id": "sg:person.014541502275.54", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014541502275.54"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Yaroslavl State University", 
              "id": "https://www.grid.ac/institutes/grid.99921.3a", 
              "name": [
                "Yaroslavl State University, 150000, Yaroslavl, Russia"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Kolesov", 
            "givenName": "A.", 
            "id": "sg:person.010035647473.20", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010035647473.20"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1023/b:joth.0000047249.39572.6d", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004715545", 
              "https://doi.org/10.1023/b:joth.0000047249.39572.6d"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4612-4050-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1014925978", 
              "https://doi.org/10.1007/978-1-4612-4050-1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4612-4050-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1014925978", 
              "https://doi.org/10.1007/978-1-4612-4050-1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.3103/s0146411613070079", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1035114088", 
              "https://doi.org/10.3103/s0146411613070079"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1515/crll.1955.194.66", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1038121119"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1134/s0965542510050076", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1039412877", 
              "https://doi.org/10.1134/s0965542510050076"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1134/s0965542510050076", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1039412877", 
              "https://doi.org/10.1134/s0965542510050076"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.3103/s0146411613070031", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049096857", 
              "https://doi.org/10.3103/s0146411613070031"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/0150099", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062840875"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2017-09", 
        "datePublishedReg": "2017-09-01", 
        "description": "In the paper we consider the problem of searching for coexisting modes in a nonlinear boundary value problem with a delay from population dynamics. For this we construct the asymptotic of spatially homogeneous cycle using the normal forms method and research the dependence of its stability on the diffusion parameter. Then we find coexisting attractors of the problem using numerical methods. Numerical experiment required an application of massively parallel computing systems and adaptation of solutions search algorithms to them. Based on the numerical analysis we come to the conclusion of the existence in the boundary value problem of solutions of two types. The first type has a simple spatial distribution and inherits the properties of a homogeneous solution. The second called the mode of self-organization is more complex distributed in space and is much more preferred in terms of population dynamics.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1134/s1995080217050110", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1136629", 
            "issn": [
              "1818-9962", 
              "1995-0802"
            ], 
            "name": "Lobachevskii Journal of Mathematics", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "5", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "38"
          }
        ], 
        "name": "Spatially inhomogeneous modes of logistic differential equation with delay and small diffusion in a flat area", 
        "pagination": "898-905", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "e45dcde82f357a6fe7a07c1756d24ce24d24f14d8276ec2dcebb69836f55e62c"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1134/s1995080217050110"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1091827339"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1134/s1995080217050110", 
          "https://app.dimensions.ai/details/publication/pub.1091827339"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-10T23:28", 
        "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_8693_00000528.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1134%2FS1995080217050110"
      }
    ]
     

    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.10.1134/s1995080217050110'

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

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1134/s1995080217050110'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1134/s1995080217050110'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1134/s1995080217050110'


     

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

    104 TRIPLES      21 PREDICATES      34 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1134/s1995080217050110 schema:about anzsrc-for:01
    2 anzsrc-for:0103
    3 schema:author Nc9b6fb0340b94c3193dbee3c6bc1802a
    4 schema:citation sg:pub.10.1007/978-1-4612-4050-1
    5 sg:pub.10.1023/b:joth.0000047249.39572.6d
    6 sg:pub.10.1134/s0965542510050076
    7 sg:pub.10.3103/s0146411613070031
    8 sg:pub.10.3103/s0146411613070079
    9 https://doi.org/10.1137/0150099
    10 https://doi.org/10.1515/crll.1955.194.66
    11 schema:datePublished 2017-09
    12 schema:datePublishedReg 2017-09-01
    13 schema:description In the paper we consider the problem of searching for coexisting modes in a nonlinear boundary value problem with a delay from population dynamics. For this we construct the asymptotic of spatially homogeneous cycle using the normal forms method and research the dependence of its stability on the diffusion parameter. Then we find coexisting attractors of the problem using numerical methods. Numerical experiment required an application of massively parallel computing systems and adaptation of solutions search algorithms to them. Based on the numerical analysis we come to the conclusion of the existence in the boundary value problem of solutions of two types. The first type has a simple spatial distribution and inherits the properties of a homogeneous solution. The second called the mode of self-organization is more complex distributed in space and is much more preferred in terms of population dynamics.
    14 schema:genre research_article
    15 schema:inLanguage en
    16 schema:isAccessibleForFree false
    17 schema:isPartOf N4b9cea2c6cb942a8b23c8f5d92dc1c97
    18 N70a9e1d9d8884ca29c51c5b34795bd7f
    19 sg:journal.1136629
    20 schema:name Spatially inhomogeneous modes of logistic differential equation with delay and small diffusion in a flat area
    21 schema:pagination 898-905
    22 schema:productId N1839f15b6b2c4d2f9696682271658eff
    23 N3de2662ad5da44cca920bf612562f237
    24 N7b852508a1744317aa2f9e4fa62c639b
    25 schema:sameAs https://app.dimensions.ai/details/publication/pub.1091827339
    26 https://doi.org/10.1134/s1995080217050110
    27 schema:sdDatePublished 2019-04-10T23:28
    28 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    29 schema:sdPublisher N21f5af1007324862af817e26f8cdfb7c
    30 schema:url http://link.springer.com/10.1134%2FS1995080217050110
    31 sgo:license sg:explorer/license/
    32 sgo:sdDataset articles
    33 rdf:type schema:ScholarlyArticle
    34 N1839f15b6b2c4d2f9696682271658eff schema:name dimensions_id
    35 schema:value pub.1091827339
    36 rdf:type schema:PropertyValue
    37 N21f5af1007324862af817e26f8cdfb7c schema:name Springer Nature - SN SciGraph project
    38 rdf:type schema:Organization
    39 N3de2662ad5da44cca920bf612562f237 schema:name readcube_id
    40 schema:value e45dcde82f357a6fe7a07c1756d24ce24d24f14d8276ec2dcebb69836f55e62c
    41 rdf:type schema:PropertyValue
    42 N4b9cea2c6cb942a8b23c8f5d92dc1c97 schema:issueNumber 5
    43 rdf:type schema:PublicationIssue
    44 N6f20a9295b854713a0a340a643fc4495 rdf:first sg:person.010035647473.20
    45 rdf:rest rdf:nil
    46 N70413016efeb40698ca863d0628af775 rdf:first sg:person.014541502275.54
    47 rdf:rest N6f20a9295b854713a0a340a643fc4495
    48 N70a9e1d9d8884ca29c51c5b34795bd7f schema:volumeNumber 38
    49 rdf:type schema:PublicationVolume
    50 N7b852508a1744317aa2f9e4fa62c639b schema:name doi
    51 schema:value 10.1134/s1995080217050110
    52 rdf:type schema:PropertyValue
    53 N8e091240faf34968a7f71764460ecea0 schema:affiliation https://www.grid.ac/institutes/grid.465407.4
    54 schema:familyName Glyzin
    55 schema:givenName S.
    56 rdf:type schema:Person
    57 Nc9b6fb0340b94c3193dbee3c6bc1802a rdf:first N8e091240faf34968a7f71764460ecea0
    58 rdf:rest N70413016efeb40698ca863d0628af775
    59 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    60 schema:name Mathematical Sciences
    61 rdf:type schema:DefinedTerm
    62 anzsrc-for:0103 schema:inDefinedTermSet anzsrc-for:
    63 schema:name Numerical and Computational Mathematics
    64 rdf:type schema:DefinedTerm
    65 sg:journal.1136629 schema:issn 1818-9962
    66 1995-0802
    67 schema:name Lobachevskii Journal of Mathematics
    68 rdf:type schema:Periodical
    69 sg:person.010035647473.20 schema:affiliation https://www.grid.ac/institutes/grid.99921.3a
    70 schema:familyName Kolesov
    71 schema:givenName A.
    72 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010035647473.20
    73 rdf:type schema:Person
    74 sg:person.014541502275.54 schema:affiliation https://www.grid.ac/institutes/grid.465407.4
    75 schema:familyName Goryunov
    76 schema:givenName V.
    77 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014541502275.54
    78 rdf:type schema:Person
    79 sg:pub.10.1007/978-1-4612-4050-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1014925978
    80 https://doi.org/10.1007/978-1-4612-4050-1
    81 rdf:type schema:CreativeWork
    82 sg:pub.10.1023/b:joth.0000047249.39572.6d schema:sameAs https://app.dimensions.ai/details/publication/pub.1004715545
    83 https://doi.org/10.1023/b:joth.0000047249.39572.6d
    84 rdf:type schema:CreativeWork
    85 sg:pub.10.1134/s0965542510050076 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039412877
    86 https://doi.org/10.1134/s0965542510050076
    87 rdf:type schema:CreativeWork
    88 sg:pub.10.3103/s0146411613070031 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049096857
    89 https://doi.org/10.3103/s0146411613070031
    90 rdf:type schema:CreativeWork
    91 sg:pub.10.3103/s0146411613070079 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035114088
    92 https://doi.org/10.3103/s0146411613070079
    93 rdf:type schema:CreativeWork
    94 https://doi.org/10.1137/0150099 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062840875
    95 rdf:type schema:CreativeWork
    96 https://doi.org/10.1515/crll.1955.194.66 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038121119
    97 rdf:type schema:CreativeWork
    98 https://www.grid.ac/institutes/grid.465407.4 schema:alternateName Scientific Center
    99 schema:name Scientific Center in Chernogolovka of Russian Academy of Sciences, 142432, Chernogolovka, Moscow oblast, Russia
    100 Yaroslavl State University, 150000, Yaroslavl, Russia
    101 rdf:type schema:Organization
    102 https://www.grid.ac/institutes/grid.99921.3a schema:alternateName Yaroslavl State University
    103 schema:name Yaroslavl State University, 150000, Yaroslavl, Russia
    104 rdf:type schema:Organization
     




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


    ...