Predator-prey models with delay and prey harvesting View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2001-09

AUTHORS

Annik Martin, Shigui Ruan

ABSTRACT

It is known that predator-prey systems with constant rate harvesting exhibit very rich dynamics. On the other hand, incorporating time delays into predator-prey models could induce instability and bifurcation. In this paper we are interested in studying the combined effects of the harvesting rate and the time delay on the dynamics of the generalized Gause-type predator-prey models and the Wangersky-Cunningham model. It is shown that in these models the time delay can cause a stable equilibrium to become unstable and even a switching of stabilities, while the harvesting rate has a stabilizing effect on the equilibrium if it is under the critical harvesting level. In particular, one of these models loses stability when the delay varies and then regains its stability when the harvesting rate is increased. Computer simulations are carried to explain the mathematical conclusions. More... »

PAGES

247-267

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s002850100095

DOI

http://dx.doi.org/10.1007/s002850100095

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1015841966

PUBMED

https://www.ncbi.nlm.nih.gov/pubmed/11681528


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"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Animals", 
        "type": "DefinedTerm"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Computer Simulation", 
        "type": "DefinedTerm"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Conservation of Natural Resources", 
        "type": "DefinedTerm"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Models, Biological", 
        "type": "DefinedTerm"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Population Dynamics", 
        "type": "DefinedTerm"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Predatory Behavior", 
        "type": "DefinedTerm"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Time Factors", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "University of New Orleans", 
          "id": "https://www.grid.ac/institutes/grid.266835.c", 
          "name": [
            "Department of Mathematics, University of New Orleans, New Orleans, LA 70148-2900, USA, US"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Martin", 
        "givenName": "Annik", 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Dalhousie University", 
          "id": "https://www.grid.ac/institutes/grid.55602.34", 
          "name": [
            "Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada. B3H 3J5. e-mail: ruan@mathstat.dal.ca, CA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Ruan", 
        "givenName": "Shigui", 
        "id": "sg:person.01063423633.28", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01063423633.28"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/bf00275221", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1001700158", 
          "https://doi.org/10.1007/bf00275221"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00275221", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1001700158", 
          "https://doi.org/10.1007/bf00275221"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00280586", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1006191577", 
          "https://doi.org/10.1007/bf00280586"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00280586", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1006191577", 
          "https://doi.org/10.1007/bf00280586"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0378-4754(93)90045-v", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1021589389"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0378-4754(93)90045-v", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1021589389"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1006/jmaa.1996.0471", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1029940712"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0040-5809(85)90028-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1033307694"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/zamm.19820621221", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1035417827"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00275152", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1036666312", 
          "https://doi.org/10.1007/bf00275152"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00275152", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1036666312", 
          "https://doi.org/10.1007/bf00275152"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0025-5564(77)90148-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1038423117"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/bimj.4710210608", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1043339631"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1017/s0334270000004227", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044653577"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-94-015-7920-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1051033171", 
          "https://doi.org/10.1007/978-94-015-7920-9"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-94-015-7920-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1051033171", 
          "https://doi.org/10.1007/978-94-015-7920-9"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/qam/1811101", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1059347702"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/s0036139994275799", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062875226"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2001-09", 
    "datePublishedReg": "2001-09-01", 
    "description": "It is known that predator-prey systems with constant rate harvesting exhibit very rich dynamics. On the other hand, incorporating time delays into predator-prey models could induce instability and bifurcation. In this paper we are interested in studying the combined effects of the harvesting rate and the time delay on the dynamics of the generalized Gause-type predator-prey models and the Wangersky-Cunningham model. It is shown that in these models the time delay can cause a stable equilibrium to become unstable and even a switching of stabilities, while the harvesting rate has a stabilizing effect on the equilibrium if it is under the critical harvesting level. In particular, one of these models loses stability when the delay varies and then regains its stability when the harvesting rate is increased. Computer simulations are carried to explain the mathematical conclusions.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s002850100095", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1081642", 
        "issn": [
          "0303-6812", 
          "1432-1416"
        ], 
        "name": "Journal of Mathematical Biology", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "3", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "43"
      }
    ], 
    "name": "Predator-prey models with delay and prey harvesting", 
    "pagination": "247-267", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "4b7bb48d706abc9482c2f1627cfcc17e376650a109ac3858dc6e2cadd5cd9bf0"
        ]
      }, 
      {
        "name": "pubmed_id", 
        "type": "PropertyValue", 
        "value": [
          "11681528"
        ]
      }, 
      {
        "name": "nlm_unique_id", 
        "type": "PropertyValue", 
        "value": [
          "7502105"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s002850100095"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1015841966"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s002850100095", 
      "https://app.dimensions.ai/details/publication/pub.1015841966"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T00:15", 
    "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_8695_00000511.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007%2Fs002850100095"
  }
]
 

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/s002850100095'

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/s002850100095'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s002850100095'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s002850100095'


 

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

149 TRIPLES      21 PREDICATES      49 URIs      28 LITERALS      16 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s002850100095 schema:about N831609a2a1b94e988078ac956e9669c8
2 Nb5e6a6c6ebcf44398caf069a48e7d86a
3 Nc7934c0a7e6c429ba51e73f7b250197c
4 Nd15b3fbd9e894b17a3cc141b019e369a
5 Ndfe2751bfd2f45c08cbe890d891d5c47
6 Neaab43e39edc4e81909b4f039c4bd3a9
7 Ned6256349e444dafafc3ef5c00122012
8 anzsrc-for:01
9 anzsrc-for:0102
10 schema:author Ne1bc38eac068495fb7f8b28a10c85875
11 schema:citation sg:pub.10.1007/978-94-015-7920-9
12 sg:pub.10.1007/bf00275152
13 sg:pub.10.1007/bf00275221
14 sg:pub.10.1007/bf00280586
15 https://doi.org/10.1002/bimj.4710210608
16 https://doi.org/10.1002/zamm.19820621221
17 https://doi.org/10.1006/jmaa.1996.0471
18 https://doi.org/10.1016/0025-5564(77)90148-1
19 https://doi.org/10.1016/0040-5809(85)90028-0
20 https://doi.org/10.1016/0378-4754(93)90045-v
21 https://doi.org/10.1017/s0334270000004227
22 https://doi.org/10.1090/qam/1811101
23 https://doi.org/10.1137/s0036139994275799
24 schema:datePublished 2001-09
25 schema:datePublishedReg 2001-09-01
26 schema:description It is known that predator-prey systems with constant rate harvesting exhibit very rich dynamics. On the other hand, incorporating time delays into predator-prey models could induce instability and bifurcation. In this paper we are interested in studying the combined effects of the harvesting rate and the time delay on the dynamics of the generalized Gause-type predator-prey models and the Wangersky-Cunningham model. It is shown that in these models the time delay can cause a stable equilibrium to become unstable and even a switching of stabilities, while the harvesting rate has a stabilizing effect on the equilibrium if it is under the critical harvesting level. In particular, one of these models loses stability when the delay varies and then regains its stability when the harvesting rate is increased. Computer simulations are carried to explain the mathematical conclusions.
27 schema:genre research_article
28 schema:inLanguage en
29 schema:isAccessibleForFree false
30 schema:isPartOf N464386b3a1bc4dccae78d1622d65f87e
31 N9d16589aafe64ba5a5c8fa260c15bc7c
32 sg:journal.1081642
33 schema:name Predator-prey models with delay and prey harvesting
34 schema:pagination 247-267
35 schema:productId N1039429d9bec4d6392b0d548e64bbca6
36 N1c390e5ce27c45f1bdcca894686dc974
37 N814c44894fe44723945c9e1688d0bb11
38 Nda592c99f3d248f7809b78ef961eee52
39 Nde014316a4cf49bbbdde0c09a9c3081f
40 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015841966
41 https://doi.org/10.1007/s002850100095
42 schema:sdDatePublished 2019-04-11T00:15
43 schema:sdLicense https://scigraph.springernature.com/explorer/license/
44 schema:sdPublisher N1c9ecb8ecc244947aa1d072f33d94f0d
45 schema:url http://link.springer.com/10.1007%2Fs002850100095
46 sgo:license sg:explorer/license/
47 sgo:sdDataset articles
48 rdf:type schema:ScholarlyArticle
49 N1039429d9bec4d6392b0d548e64bbca6 schema:name readcube_id
50 schema:value 4b7bb48d706abc9482c2f1627cfcc17e376650a109ac3858dc6e2cadd5cd9bf0
51 rdf:type schema:PropertyValue
52 N192cfa96a9814ce197b9a9dfcfed9587 rdf:first sg:person.01063423633.28
53 rdf:rest rdf:nil
54 N1c390e5ce27c45f1bdcca894686dc974 schema:name doi
55 schema:value 10.1007/s002850100095
56 rdf:type schema:PropertyValue
57 N1c9ecb8ecc244947aa1d072f33d94f0d schema:name Springer Nature - SN SciGraph project
58 rdf:type schema:Organization
59 N464386b3a1bc4dccae78d1622d65f87e schema:volumeNumber 43
60 rdf:type schema:PublicationVolume
61 N814c44894fe44723945c9e1688d0bb11 schema:name dimensions_id
62 schema:value pub.1015841966
63 rdf:type schema:PropertyValue
64 N831609a2a1b94e988078ac956e9669c8 schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
65 schema:name Population Dynamics
66 rdf:type schema:DefinedTerm
67 N9d16589aafe64ba5a5c8fa260c15bc7c schema:issueNumber 3
68 rdf:type schema:PublicationIssue
69 Nb5e6a6c6ebcf44398caf069a48e7d86a schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
70 schema:name Conservation of Natural Resources
71 rdf:type schema:DefinedTerm
72 Nc7934c0a7e6c429ba51e73f7b250197c schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
73 schema:name Computer Simulation
74 rdf:type schema:DefinedTerm
75 Nd15b3fbd9e894b17a3cc141b019e369a schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
76 schema:name Animals
77 rdf:type schema:DefinedTerm
78 Nda592c99f3d248f7809b78ef961eee52 schema:name nlm_unique_id
79 schema:value 7502105
80 rdf:type schema:PropertyValue
81 Nde014316a4cf49bbbdde0c09a9c3081f schema:name pubmed_id
82 schema:value 11681528
83 rdf:type schema:PropertyValue
84 Ndfe2751bfd2f45c08cbe890d891d5c47 schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
85 schema:name Time Factors
86 rdf:type schema:DefinedTerm
87 Ne1bc38eac068495fb7f8b28a10c85875 rdf:first Nfb9c4bc40cb3483fbd826b607a0c7fcf
88 rdf:rest N192cfa96a9814ce197b9a9dfcfed9587
89 Neaab43e39edc4e81909b4f039c4bd3a9 schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
90 schema:name Models, Biological
91 rdf:type schema:DefinedTerm
92 Ned6256349e444dafafc3ef5c00122012 schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
93 schema:name Predatory Behavior
94 rdf:type schema:DefinedTerm
95 Nfb9c4bc40cb3483fbd826b607a0c7fcf schema:affiliation https://www.grid.ac/institutes/grid.266835.c
96 schema:familyName Martin
97 schema:givenName Annik
98 rdf:type schema:Person
99 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
100 schema:name Mathematical Sciences
101 rdf:type schema:DefinedTerm
102 anzsrc-for:0102 schema:inDefinedTermSet anzsrc-for:
103 schema:name Applied Mathematics
104 rdf:type schema:DefinedTerm
105 sg:journal.1081642 schema:issn 0303-6812
106 1432-1416
107 schema:name Journal of Mathematical Biology
108 rdf:type schema:Periodical
109 sg:person.01063423633.28 schema:affiliation https://www.grid.ac/institutes/grid.55602.34
110 schema:familyName Ruan
111 schema:givenName Shigui
112 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01063423633.28
113 rdf:type schema:Person
114 sg:pub.10.1007/978-94-015-7920-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051033171
115 https://doi.org/10.1007/978-94-015-7920-9
116 rdf:type schema:CreativeWork
117 sg:pub.10.1007/bf00275152 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036666312
118 https://doi.org/10.1007/bf00275152
119 rdf:type schema:CreativeWork
120 sg:pub.10.1007/bf00275221 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001700158
121 https://doi.org/10.1007/bf00275221
122 rdf:type schema:CreativeWork
123 sg:pub.10.1007/bf00280586 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006191577
124 https://doi.org/10.1007/bf00280586
125 rdf:type schema:CreativeWork
126 https://doi.org/10.1002/bimj.4710210608 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043339631
127 rdf:type schema:CreativeWork
128 https://doi.org/10.1002/zamm.19820621221 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035417827
129 rdf:type schema:CreativeWork
130 https://doi.org/10.1006/jmaa.1996.0471 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029940712
131 rdf:type schema:CreativeWork
132 https://doi.org/10.1016/0025-5564(77)90148-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038423117
133 rdf:type schema:CreativeWork
134 https://doi.org/10.1016/0040-5809(85)90028-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033307694
135 rdf:type schema:CreativeWork
136 https://doi.org/10.1016/0378-4754(93)90045-v schema:sameAs https://app.dimensions.ai/details/publication/pub.1021589389
137 rdf:type schema:CreativeWork
138 https://doi.org/10.1017/s0334270000004227 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044653577
139 rdf:type schema:CreativeWork
140 https://doi.org/10.1090/qam/1811101 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059347702
141 rdf:type schema:CreativeWork
142 https://doi.org/10.1137/s0036139994275799 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062875226
143 rdf:type schema:CreativeWork
144 https://www.grid.ac/institutes/grid.266835.c schema:alternateName University of New Orleans
145 schema:name Department of Mathematics, University of New Orleans, New Orleans, LA 70148-2900, USA, US
146 rdf:type schema:Organization
147 https://www.grid.ac/institutes/grid.55602.34 schema:alternateName Dalhousie University
148 schema:name Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada. B3H 3J5. e-mail: ruan@mathstat.dal.ca, CA
149 rdf:type schema:Organization
 




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


...