Backward bifurcation of predator–prey model with anti-predator behaviors View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2019-12

AUTHORS

Guangyao Tang, Wenjie Qin

ABSTRACT

In this study, we consider a predator–prey model with stage structure and anti-predator behavior such that the adult prey can counterattack their predators. We first investigate the existence and stability of the equilibria. Especially, we verify that there can exist at most one positive equilibrium, which is always stable whenever it exists, if the predator only feed on one age class. We then prove that the system can undergo either a forward bifurcation or a backward bifurcation. Numerical analyses show that anti-predator behavior is beneficial to the growth of prey population, especially helps the equilibrium level of the prey population increase, by enhancing the pressure on the predator. Moreover, anti-predator behavior makes the coexistence of the predator and prey less likely by shrinking the coexistence region with respect to the initial conditions or weakening the existence and stability of the positive equilibrium. More... »

PAGES

8

Identifiers

URI

http://scigraph.springernature.com/pub.10.1186/s13662-019-1944-4

DOI

http://dx.doi.org/10.1186/s13662-019-1944-4

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1111319528


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/2008/0602", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Ecology", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/06", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Biological Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Hubei University for Nationalities", 
          "id": "https://www.grid.ac/institutes/grid.440771.1", 
          "name": [
            "Department of Mathematics, Hubei University for Nationalities, Enshi, P.R. China"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Tang", 
        "givenName": "Guangyao", 
        "id": "sg:person.016701175376.30", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016701175376.30"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "China Three Gorges University", 
          "id": "https://www.grid.ac/institutes/grid.254148.e", 
          "name": [
            "Three Gorges Mathematical Research Center, China Three Gorges University, Yichang, P.R. China"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Qin", 
        "givenName": "Wenjie", 
        "id": "sg:person.07700507011.37", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07700507011.37"
        ], 
        "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": "https://doi.org/10.1016/j.nonrwa.2009.10.001", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1005407322"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1155/2009/285934", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1005426762", 
          "https://doi.org/10.1155/2009/285934"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0040-5809(83)90023-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1005837186"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.mbs.2016.12.005", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1010352403"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0025-5564(90)90019-u", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1010859356"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0025-5564(00)00033-x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1015345344"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01896254", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1019073586", 
          "https://doi.org/10.1007/bf01896254"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01896254", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1019073586", 
          "https://doi.org/10.1007/bf01896254"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.amc.2011.03.139", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1022087589"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.amc.2006.05.025", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1022093165"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1186/s13662-015-0661-x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1022304515", 
          "https://doi.org/10.1186/s13662-015-0661-x"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1186/s13662-015-0661-x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1022304515", 
          "https://doi.org/10.1186/s13662-015-0661-x"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.nonrwa.2009.01.001", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1022448356"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.mcm.2006.04.001", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1023543919"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jmaa.2004.05.045", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1026773313"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0025-5564(02)00108-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1029513709"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01193354", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1029663049", 
          "https://doi.org/10.1007/bf01193354"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01193354", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1029663049", 
          "https://doi.org/10.1007/bf01193354"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10114-002-0234-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1030193086", 
          "https://doi.org/10.1007/s10114-002-0234-2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10114-002-0234-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1030193086", 
          "https://doi.org/10.1007/s10114-002-0234-2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1046/j.1461-0248.2002.00349.x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1030824017"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.na.2012.08.013", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1034902082"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1038/srep00728", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1035885124", 
          "https://doi.org/10.1038/srep00728"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.tpb.2005.05.004", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1040948160"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0898-1221(97)00056-4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1042448179"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1023/a:1017049719721", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1042678351", 
          "https://doi.org/10.1023/a:1017049719721"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.nonrwa.2013.02.007", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044030131"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.nonrwa.2006.09.009", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044167662"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1016/s0092-8240(03)00005-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044284202", 
          "https://doi.org/10.1016/s0092-8240(03)00005-3"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.mbs.2005.12.022", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1047415200"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.amc.2015.07.109", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1048982805"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.chaos.2014.11.008", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1050598533"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.amc.2006.05.195", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1052589478"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1086/284719", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058594842"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1086/285989", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058596112"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1086/303189", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058610728"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1086/321321", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058623487"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/050627757", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062846118"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/050630003", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062846198"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/060670377", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062849716"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/110847020", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062865301"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/s0036139901397285", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062874774"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/s0036139999361896", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062875696"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.3934/dcdsb.2004.4.547", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1071735948"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1142/s0218127418500992", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1106072041"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2019-12", 
    "datePublishedReg": "2019-12-01", 
    "description": "In this study, we consider a predator\u2013prey model with stage structure and anti-predator behavior such that the adult prey can counterattack their predators. We first investigate the existence and stability of the equilibria. Especially, we verify that there can exist at most one positive equilibrium, which is always stable whenever it exists, if the predator only feed on one age class. We then prove that the system can undergo either a forward bifurcation or a backward bifurcation. Numerical analyses show that anti-predator behavior is beneficial to the growth of prey population, especially helps the equilibrium level of the prey population increase, by enhancing the pressure on the predator. Moreover, anti-predator behavior makes the coexistence of the predator and prey less likely by shrinking the coexistence region with respect to the initial conditions or weakening the existence and stability of the positive equilibrium.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1186/s13662-019-1944-4", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": true, 
    "isPartOf": [
      {
        "id": "sg:journal.1052613", 
        "issn": [
          "1687-1839", 
          "1687-1847"
        ], 
        "name": "Advances in Difference Equations", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "2019"
      }
    ], 
    "name": "Backward bifurcation of predator\u2013prey model with anti-predator behaviors", 
    "pagination": "8", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "54fca9d91085b2b1053f93398c1792677c7dcfc96c9224bdccd4faf6aabff89f"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1186/s13662-019-1944-4"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1111319528"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1186/s13662-019-1944-4", 
      "https://app.dimensions.ai/details/publication/pub.1111319528"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T08:37", 
    "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/v90/0000000315_0000000315/records_6313_00000000.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://link.springer.com/10.1186%2Fs13662-019-1944-4"
  }
]
 

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.10.1186/s13662-019-1944-4'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1186/s13662-019-1944-4'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1186/s13662-019-1944-4'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1186/s13662-019-1944-4'


 

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

206 TRIPLES      21 PREDICATES      69 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1186/s13662-019-1944-4 schema:about anzsrc-for:06
2 anzsrc-for:0602
3 schema:author N9fedb9f53a104bbb8253c7a3add2af3a
4 schema:citation sg:pub.10.1007/bf00275221
5 sg:pub.10.1007/bf01193354
6 sg:pub.10.1007/bf01896254
7 sg:pub.10.1007/s10114-002-0234-2
8 sg:pub.10.1016/s0092-8240(03)00005-3
9 sg:pub.10.1023/a:1017049719721
10 sg:pub.10.1038/srep00728
11 sg:pub.10.1155/2009/285934
12 sg:pub.10.1186/s13662-015-0661-x
13 https://doi.org/10.1016/0025-5564(90)90019-u
14 https://doi.org/10.1016/0040-5809(83)90023-0
15 https://doi.org/10.1016/j.amc.2006.05.025
16 https://doi.org/10.1016/j.amc.2006.05.195
17 https://doi.org/10.1016/j.amc.2011.03.139
18 https://doi.org/10.1016/j.amc.2015.07.109
19 https://doi.org/10.1016/j.chaos.2014.11.008
20 https://doi.org/10.1016/j.jmaa.2004.05.045
21 https://doi.org/10.1016/j.mbs.2005.12.022
22 https://doi.org/10.1016/j.mbs.2016.12.005
23 https://doi.org/10.1016/j.mcm.2006.04.001
24 https://doi.org/10.1016/j.na.2012.08.013
25 https://doi.org/10.1016/j.nonrwa.2006.09.009
26 https://doi.org/10.1016/j.nonrwa.2009.01.001
27 https://doi.org/10.1016/j.nonrwa.2009.10.001
28 https://doi.org/10.1016/j.nonrwa.2013.02.007
29 https://doi.org/10.1016/j.tpb.2005.05.004
30 https://doi.org/10.1016/s0025-5564(00)00033-x
31 https://doi.org/10.1016/s0025-5564(02)00108-6
32 https://doi.org/10.1016/s0898-1221(97)00056-4
33 https://doi.org/10.1046/j.1461-0248.2002.00349.x
34 https://doi.org/10.1086/284719
35 https://doi.org/10.1086/285989
36 https://doi.org/10.1086/303189
37 https://doi.org/10.1086/321321
38 https://doi.org/10.1137/050627757
39 https://doi.org/10.1137/050630003
40 https://doi.org/10.1137/060670377
41 https://doi.org/10.1137/110847020
42 https://doi.org/10.1137/s0036139901397285
43 https://doi.org/10.1137/s0036139999361896
44 https://doi.org/10.1142/s0218127418500992
45 https://doi.org/10.3934/dcdsb.2004.4.547
46 schema:datePublished 2019-12
47 schema:datePublishedReg 2019-12-01
48 schema:description In this study, we consider a predator–prey model with stage structure and anti-predator behavior such that the adult prey can counterattack their predators. We first investigate the existence and stability of the equilibria. Especially, we verify that there can exist at most one positive equilibrium, which is always stable whenever it exists, if the predator only feed on one age class. We then prove that the system can undergo either a forward bifurcation or a backward bifurcation. Numerical analyses show that anti-predator behavior is beneficial to the growth of prey population, especially helps the equilibrium level of the prey population increase, by enhancing the pressure on the predator. Moreover, anti-predator behavior makes the coexistence of the predator and prey less likely by shrinking the coexistence region with respect to the initial conditions or weakening the existence and stability of the positive equilibrium.
49 schema:genre research_article
50 schema:inLanguage en
51 schema:isAccessibleForFree true
52 schema:isPartOf N6adcc2f3770b4f689f40e92aa73eccfa
53 Nbcdca47ab8f4439ba3366c6c722d423e
54 sg:journal.1052613
55 schema:name Backward bifurcation of predator–prey model with anti-predator behaviors
56 schema:pagination 8
57 schema:productId N2f229aba1a9343c1b842cf0d22c95183
58 Nb9a64b02195d48b5ab90511956be0fbf
59 Ne79e4e668db54befa5e4b8ebfd26d54d
60 schema:sameAs https://app.dimensions.ai/details/publication/pub.1111319528
61 https://doi.org/10.1186/s13662-019-1944-4
62 schema:sdDatePublished 2019-04-11T08:37
63 schema:sdLicense https://scigraph.springernature.com/explorer/license/
64 schema:sdPublisher Nfd4d26a9b84a400aa5fdd548c0d1d2f2
65 schema:url https://link.springer.com/10.1186%2Fs13662-019-1944-4
66 sgo:license sg:explorer/license/
67 sgo:sdDataset articles
68 rdf:type schema:ScholarlyArticle
69 N2f229aba1a9343c1b842cf0d22c95183 schema:name doi
70 schema:value 10.1186/s13662-019-1944-4
71 rdf:type schema:PropertyValue
72 N56b679c8d5b14995985690c91442d421 rdf:first sg:person.07700507011.37
73 rdf:rest rdf:nil
74 N6adcc2f3770b4f689f40e92aa73eccfa schema:issueNumber 1
75 rdf:type schema:PublicationIssue
76 N9fedb9f53a104bbb8253c7a3add2af3a rdf:first sg:person.016701175376.30
77 rdf:rest N56b679c8d5b14995985690c91442d421
78 Nb9a64b02195d48b5ab90511956be0fbf schema:name readcube_id
79 schema:value 54fca9d91085b2b1053f93398c1792677c7dcfc96c9224bdccd4faf6aabff89f
80 rdf:type schema:PropertyValue
81 Nbcdca47ab8f4439ba3366c6c722d423e schema:volumeNumber 2019
82 rdf:type schema:PublicationVolume
83 Ne79e4e668db54befa5e4b8ebfd26d54d schema:name dimensions_id
84 schema:value pub.1111319528
85 rdf:type schema:PropertyValue
86 Nfd4d26a9b84a400aa5fdd548c0d1d2f2 schema:name Springer Nature - SN SciGraph project
87 rdf:type schema:Organization
88 anzsrc-for:06 schema:inDefinedTermSet anzsrc-for:
89 schema:name Biological Sciences
90 rdf:type schema:DefinedTerm
91 anzsrc-for:0602 schema:inDefinedTermSet anzsrc-for:
92 schema:name Ecology
93 rdf:type schema:DefinedTerm
94 sg:journal.1052613 schema:issn 1687-1839
95 1687-1847
96 schema:name Advances in Difference Equations
97 rdf:type schema:Periodical
98 sg:person.016701175376.30 schema:affiliation https://www.grid.ac/institutes/grid.440771.1
99 schema:familyName Tang
100 schema:givenName Guangyao
101 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016701175376.30
102 rdf:type schema:Person
103 sg:person.07700507011.37 schema:affiliation https://www.grid.ac/institutes/grid.254148.e
104 schema:familyName Qin
105 schema:givenName Wenjie
106 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07700507011.37
107 rdf:type schema:Person
108 sg:pub.10.1007/bf00275221 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001700158
109 https://doi.org/10.1007/bf00275221
110 rdf:type schema:CreativeWork
111 sg:pub.10.1007/bf01193354 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029663049
112 https://doi.org/10.1007/bf01193354
113 rdf:type schema:CreativeWork
114 sg:pub.10.1007/bf01896254 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019073586
115 https://doi.org/10.1007/bf01896254
116 rdf:type schema:CreativeWork
117 sg:pub.10.1007/s10114-002-0234-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030193086
118 https://doi.org/10.1007/s10114-002-0234-2
119 rdf:type schema:CreativeWork
120 sg:pub.10.1016/s0092-8240(03)00005-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044284202
121 https://doi.org/10.1016/s0092-8240(03)00005-3
122 rdf:type schema:CreativeWork
123 sg:pub.10.1023/a:1017049719721 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042678351
124 https://doi.org/10.1023/a:1017049719721
125 rdf:type schema:CreativeWork
126 sg:pub.10.1038/srep00728 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035885124
127 https://doi.org/10.1038/srep00728
128 rdf:type schema:CreativeWork
129 sg:pub.10.1155/2009/285934 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005426762
130 https://doi.org/10.1155/2009/285934
131 rdf:type schema:CreativeWork
132 sg:pub.10.1186/s13662-015-0661-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1022304515
133 https://doi.org/10.1186/s13662-015-0661-x
134 rdf:type schema:CreativeWork
135 https://doi.org/10.1016/0025-5564(90)90019-u schema:sameAs https://app.dimensions.ai/details/publication/pub.1010859356
136 rdf:type schema:CreativeWork
137 https://doi.org/10.1016/0040-5809(83)90023-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005837186
138 rdf:type schema:CreativeWork
139 https://doi.org/10.1016/j.amc.2006.05.025 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022093165
140 rdf:type schema:CreativeWork
141 https://doi.org/10.1016/j.amc.2006.05.195 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052589478
142 rdf:type schema:CreativeWork
143 https://doi.org/10.1016/j.amc.2011.03.139 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022087589
144 rdf:type schema:CreativeWork
145 https://doi.org/10.1016/j.amc.2015.07.109 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048982805
146 rdf:type schema:CreativeWork
147 https://doi.org/10.1016/j.chaos.2014.11.008 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050598533
148 rdf:type schema:CreativeWork
149 https://doi.org/10.1016/j.jmaa.2004.05.045 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026773313
150 rdf:type schema:CreativeWork
151 https://doi.org/10.1016/j.mbs.2005.12.022 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047415200
152 rdf:type schema:CreativeWork
153 https://doi.org/10.1016/j.mbs.2016.12.005 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010352403
154 rdf:type schema:CreativeWork
155 https://doi.org/10.1016/j.mcm.2006.04.001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023543919
156 rdf:type schema:CreativeWork
157 https://doi.org/10.1016/j.na.2012.08.013 schema:sameAs https://app.dimensions.ai/details/publication/pub.1034902082
158 rdf:type schema:CreativeWork
159 https://doi.org/10.1016/j.nonrwa.2006.09.009 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044167662
160 rdf:type schema:CreativeWork
161 https://doi.org/10.1016/j.nonrwa.2009.01.001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022448356
162 rdf:type schema:CreativeWork
163 https://doi.org/10.1016/j.nonrwa.2009.10.001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005407322
164 rdf:type schema:CreativeWork
165 https://doi.org/10.1016/j.nonrwa.2013.02.007 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044030131
166 rdf:type schema:CreativeWork
167 https://doi.org/10.1016/j.tpb.2005.05.004 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040948160
168 rdf:type schema:CreativeWork
169 https://doi.org/10.1016/s0025-5564(00)00033-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1015345344
170 rdf:type schema:CreativeWork
171 https://doi.org/10.1016/s0025-5564(02)00108-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029513709
172 rdf:type schema:CreativeWork
173 https://doi.org/10.1016/s0898-1221(97)00056-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042448179
174 rdf:type schema:CreativeWork
175 https://doi.org/10.1046/j.1461-0248.2002.00349.x schema:sameAs https://app.dimensions.ai/details/publication/pub.1030824017
176 rdf:type schema:CreativeWork
177 https://doi.org/10.1086/284719 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058594842
178 rdf:type schema:CreativeWork
179 https://doi.org/10.1086/285989 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058596112
180 rdf:type schema:CreativeWork
181 https://doi.org/10.1086/303189 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058610728
182 rdf:type schema:CreativeWork
183 https://doi.org/10.1086/321321 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058623487
184 rdf:type schema:CreativeWork
185 https://doi.org/10.1137/050627757 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062846118
186 rdf:type schema:CreativeWork
187 https://doi.org/10.1137/050630003 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062846198
188 rdf:type schema:CreativeWork
189 https://doi.org/10.1137/060670377 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062849716
190 rdf:type schema:CreativeWork
191 https://doi.org/10.1137/110847020 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062865301
192 rdf:type schema:CreativeWork
193 https://doi.org/10.1137/s0036139901397285 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062874774
194 rdf:type schema:CreativeWork
195 https://doi.org/10.1137/s0036139999361896 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062875696
196 rdf:type schema:CreativeWork
197 https://doi.org/10.1142/s0218127418500992 schema:sameAs https://app.dimensions.ai/details/publication/pub.1106072041
198 rdf:type schema:CreativeWork
199 https://doi.org/10.3934/dcdsb.2004.4.547 schema:sameAs https://app.dimensions.ai/details/publication/pub.1071735948
200 rdf:type schema:CreativeWork
201 https://www.grid.ac/institutes/grid.254148.e schema:alternateName China Three Gorges University
202 schema:name Three Gorges Mathematical Research Center, China Three Gorges University, Yichang, P.R. China
203 rdf:type schema:Organization
204 https://www.grid.ac/institutes/grid.440771.1 schema:alternateName Hubei University for Nationalities
205 schema:name Department of Mathematics, Hubei University for Nationalities, Enshi, P.R. China
206 rdf:type schema:Organization
 




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


...