Dynamical Behavior of a Delayed Holling Type-II Predator-Prey Model with Predator Cannibalism

In this article, we propose the Holling type-II predator-prey model involving cannibalism and gestation delay in predators. We study the existence of all possible equilibrium points of the proposed model. We give the condition for the local stability and Hopf bifurcation analysis for the nondelayed...

Full description

Saved in:
Bibliographic Details
Published inJournal of Mathematics Vol. 2022; no. 1
Main Authors Lavanya, R., Vinoth, S., Sathiyanathan, K., Njitacke Tabekoueng, Zeric, Hammachukiattikul, P., Vadivel, R.
Format Journal Article
LanguageEnglish
Published Cairo Hindawi 2022
John Wiley & Sons, Inc
Wiley
Subjects
Cannibalism
Endangered & extinct species
Equilibrium
Extinction
Hopf bifurcation
Mathematics
Population
Predator-prey simulation
Predators
Stability analysis
Online AccessGet full text

Cover

Abstract In this article, we propose the Holling type-II predator-prey model involving cannibalism and gestation delay in predators. We study the existence of all possible equilibrium points of the proposed model. We give the condition for the local stability and Hopf bifurcation analysis for the nondelayed model. Next, we also establish the local stability and Hopf bifurcation analysis for the corresponding delayed model. Finally, we discuss how cannibalism and delay play an important role in stabilizing and destabilizing the proposed system both theoretically and numerically.
AbstractList In this article, we propose the Holling type-II predator-prey model involving cannibalism and gestation delay in predators. We study the existence of all possible equilibrium points of the proposed model. We give the condition for the local stability and Hopf bifurcation analysis for the nondelayed model. Next, we also establish the local stability and Hopf bifurcation analysis for the corresponding delayed model. Finally, we discuss how cannibalism and delay play an important role in stabilizing and destabilizing the proposed system both theoretically and numerically.
Audience Academic
Author Vadivel, R.
Sathiyanathan, K.
Vinoth, S.
Hammachukiattikul, P.
Njitacke Tabekoueng, Zeric
Lavanya, R.
Author_xml – sequence: 1
  givenname: R.
  surname: Lavanya
  fullname: Lavanya, R.
  organization: Department of MathematicsSRMV College of Arts and ScienceCoimbatoreTamil NaduIndia
– sequence: 2
  givenname: S.
  orcidid: 0000-0002-4509-9484
  surname: Vinoth
  fullname: Vinoth, S.
  organization: Department of Computer ScienceKGiSL Institute of Information ManagementCoimbatoreTamil NaduIndia
– sequence: 3
  givenname: K.
  orcidid: 0000-0002-3994-3896
  surname: Sathiyanathan
  fullname: Sathiyanathan, K.
  organization: Department of MathematicsSRMV College of Arts and ScienceCoimbatoreTamil NaduIndia
– sequence: 4
  givenname: Zeric
  orcidid: 0000-0001-7797-8929
  surname: Njitacke Tabekoueng
  fullname: Njitacke Tabekoueng, Zeric
  organization: Department of Electrical and Electronic EngineeringCollege of Technology (COT)University of BueaP.O. Box 63BueaCameroonubuea.cm
– sequence: 5
  givenname: P.
  orcidid: 0000-0003-0267-110X
  surname: Hammachukiattikul
  fullname: Hammachukiattikul, P.
  organization: Department of MathematicsPhuket Rajabhat UniversityPhuket-83000Thailandpkru.ac.th
– sequence: 6
  givenname: R.
  orcidid: 0000-0002-1385-5345
  surname: Vadivel
  fullname: Vadivel, R.
  organization: Department of MathematicsPhuket Rajabhat UniversityPhuket-83000Thailandpkru.ac.th
BookMark eNp9UctuEzEUtVArUUp3fIAlljCtn7FnWVKgkYraRVki647tSRw5dvBMW83f45BSBILKi_vwOede-7xCByknj9AbSk4plfKMEcbOBFGUK_kCHTFORSOUlge_8hlrX6KTYVgTQijTXLfkCH27mBJsgoWIP_gV3IdccO4x4AsfYfIOX-YYQ1ri22nrm8UC3xTvYMylqcmEv2TnI34I4-rpAs8hpdBBDMPmNTrsIQ7-5DEeo6-fPt7OL5ur68-L-flVY4UiY-OkZI57wYnmrXO987YXbSuF7ewMVO8pgAQnnW1F58SMcmpdq50AZoWt5TFa7HVdhrXZlrCBMpkMwfxs5LI0UMZgozdeyFZarnSnhZDAWm4lE5TITnKh9U7r7V5rW_L3Oz-MZp3vSqrrG6aoklQRIX-jllBFQ-rzWMBuwmDNueacSkoUq6jTf6Dqcb7-efWvD7X_B-H9nmBLHobi-6fHUGJ2NpudzebR5gpnf8FtGGEMOdU5If6P9G5PWoXk4CE8P-IHKyu1Bg
CitedBy_id crossref_primary_10_1155_2024_8120170
crossref_primary_10_1002_zamm_202300441
crossref_primary_10_1155_jama_5535248
crossref_primary_10_1186_s13661_023_01770_x
crossref_primary_10_1155_2024_5782500
Cites_doi 10.1142/s1793524518500109
10.1186/s13662-020-02579-z
10.1007/b98868
10.1016/s0960-0779(02)00079-6
10.1186/s13662-021-03490-x
10.1016/j.ecocom.2015.12.001
10.1155/2020/7306412
10.3934/mbe.2019121
10.1142/s1793524522500140
10.1007/978-981-16-0626-7
10.1186/s13662-021-03216-z
10.1007/s11071-016-2844-8
10.1016/j.ecocom.2014.01.004
10.1155/2022/6931354
10.1098/rspb.2003.2555
10.1016/j.amc.2020.125919
10.3934/dcdss.2020468
10.1016/j.chaos.2021.111212
10.1007/s12555-020-0526-2
10.1186/s13662-020-02609-w
10.1142/s0218127415501230
10.1086/282272
10.1007/s00285-005-0342-6
10.1016/j.amc.2019.03.034
10.1186/s13662-019-2289-8
ContentType Journal Article
Copyright Copyright © 2022 R. Lavanya et al.
COPYRIGHT 2022 John Wiley & Sons, Inc.
Copyright © 2022 R. Lavanya et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0
Copyright_xml – notice: Copyright © 2022 R. Lavanya et al.
– notice: COPYRIGHT 2022 John Wiley & Sons, Inc.
– notice: Copyright © 2022 R. Lavanya et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0
DBID RHU
RHW
RHX
AAYXX
CITATION
3V.
7SC
7TB
7XB
8AL
8FD
8FE
8FG
8FK
ABJCF
ABUWG
AFKRA
ARAPS
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
FR3
GNUQQ
HCIFZ
JQ2
K7-
KR7
L6V
L7M
L~C
L~D
M0N
M7S
P62
PHGZM
PHGZT
PIMPY
PKEHL
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
PTHSS
Q9U
DOA
DOI 10.1155/2022/4071375
DatabaseName Hindawi Publishing Complete
Hindawi Publishing Subscription Journals
Hindawi Publishing Open Access
CrossRef
ProQuest Central (Corporate)
Computer and Information Systems Abstracts
Mechanical & Transportation Engineering Abstracts
ProQuest Central (purchase pre-March 2016)
Computing Database (Alumni Edition)
Technology Research Database
ProQuest SciTech Collection
ProQuest Technology Collection
ProQuest Central (Alumni) (purchase pre-March 2016)
Materials Science & Engineering Collection
ProQuest Central (Alumni)
ProQuest Central UK/Ireland
Advanced Technologies & Aerospace Collection
ProQuest Central Essentials
ProQuest Central
Technology Collection
ProQuest One Community College
ProQuest Central Korea
Engineering Research Database
ProQuest Central Student
SciTech Premium Collection
ProQuest Computer Science Collection
Computer Science Database
Civil Engineering Abstracts
ProQuest Engineering Collection
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
Computing Database
Engineering Database
ProQuest Advanced Technologies & Aerospace Collection
ProQuest Central Premium
ProQuest One Academic (New)
ProQuest Publicly Available Content Database
ProQuest One Academic Middle East (New)
ProQuest One Academic Eastern Edition (DO NOT USE)
ProQuest One Applied & Life Sciences
ProQuest One Academic
ProQuest One Academic UKI Edition
ProQuest Central China
Engineering collection
ProQuest Central Basic
DOAJ Directory of Open Access Journals
DatabaseTitle CrossRef
Publicly Available Content Database
Computer Science Database
ProQuest Central Student
Technology Collection
Technology Research Database
Computer and Information Systems Abstracts – Academic
ProQuest One Academic Middle East (New)
Mechanical & Transportation Engineering Abstracts
ProQuest Advanced Technologies & Aerospace Collection
ProQuest Central Essentials
ProQuest Computer Science Collection
Computer and Information Systems Abstracts
ProQuest Central (Alumni Edition)
SciTech Premium Collection
ProQuest One Community College
ProQuest Central China
ProQuest Central
ProQuest One Applied & Life Sciences
ProQuest Engineering Collection
ProQuest Central Korea
ProQuest Central (New)
Advanced Technologies Database with Aerospace
Engineering Collection
Advanced Technologies & Aerospace Collection
Civil Engineering Abstracts
ProQuest Computing
Engineering Database
ProQuest Central Basic
ProQuest Computing (Alumni Edition)
ProQuest One Academic Eastern Edition
ProQuest Technology Collection
ProQuest SciTech Collection
Computer and Information Systems Abstracts Professional
ProQuest One Academic UKI Edition
Materials Science & Engineering Collection
Engineering Research Database
ProQuest One Academic
ProQuest One Academic (New)
ProQuest Central (Alumni)
DatabaseTitleList


Publicly Available Content Database
CrossRef
Database_xml – sequence: 1
  dbid: RHX
  name: Hindawi Publishing Open Access
  url: http://www.hindawi.com/journals/
  sourceTypes: Publisher
– sequence: 2
  dbid: DOA
  name: DOAJ Directory of Open Access Journals
  url: https://www.doaj.org/
  sourceTypes: Open Website
– sequence: 3
  dbid: 8FG
  name: ProQuest Technology Collection
  url: https://search.proquest.com/technologycollection1
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISSN 2314-4785
Editor Yildirim, Kenan
Editor_xml – sequence: 1
  givenname: Kenan
  surname: Yildirim
  fullname: Yildirim, Kenan
ExternalDocumentID oai_doaj_org_article_e4595c378b8445a293c524105b534881
A833151072
10_1155_2022_4071375
GroupedDBID 3V.
4.4
5VS
8FE
8FG
AAFWJ
AAJEY
ABJCF
ABUWG
ACIPV
ACIWK
ADBBV
AFKRA
AFPKN
ALMA_UNASSIGNED_HOLDINGS
ARAPS
AZQEC
BCNDV
BENPR
BGLVJ
BPHCQ
CCPQU
DWQXO
EBS
ESX
GNUQQ
GROUPED_DOAJ
HCIFZ
IAO
IHR
K6V
K7-
KQ8
L6V
M0N
M7S
OK1
PIMPY
PQQKQ
PROAC
PTHSS
RHU
RHW
RHX
0R~
24P
AAYXX
ACCMX
AMVHM
CITATION
EJD
H13
ITC
PHGZM
PHGZT
M~E
7SC
7TB
7XB
8AL
8FD
8FK
AAMMB
AEFGJ
AGXDD
AIDQK
AIDYY
FR3
JQ2
KR7
L7M
L~C
L~D
P62
PKEHL
PQEST
PQGLB
PQUKI
PRINS
Q9U
PUEGO
ID FETCH-LOGICAL-c470t-d552d3e430839ddfdecf49954cbc6a7fe1aa5ad5dc94bd46131cd98d4a2c4c613
IEDL.DBID BENPR
ISSN 2314-4629
IngestDate Wed Aug 27 01:31:44 EDT 2025
Fri Jul 25 12:01:25 EDT 2025
Wed Apr 02 17:06:40 EDT 2025
Tue Apr 01 03:55:59 EDT 2025
Thu Apr 24 23:06:36 EDT 2025
Tue Jul 01 04:01:36 EDT 2025
Sun Jun 02 18:53:29 EDT 2024
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 1
Language English
License This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c470t-d552d3e430839ddfdecf49954cbc6a7fe1aa5ad5dc94bd46131cd98d4a2c4c613
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0000-0002-3994-3896
0000-0003-0267-110X
0000-0002-1385-5345
0000-0002-4509-9484
0000-0001-7797-8929
OpenAccessLink https://www.proquest.com/docview/2717517045?pq-origsite=%requestingapplication%
PQID 2717517045
PQPubID 2037347
ParticipantIDs doaj_primary_oai_doaj_org_article_e4595c378b8445a293c524105b534881
proquest_journals_2717517045
gale_infotracmisc_A833151072
gale_infotracacademiconefile_A833151072
crossref_primary_10_1155_2022_4071375
crossref_citationtrail_10_1155_2022_4071375
hindawi_primary_10_1155_2022_4071375
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2022-00-00
PublicationDateYYYYMMDD 2022-01-01
PublicationDate_xml – year: 2022
  text: 2022-00-00
PublicationDecade 2020
PublicationPlace Cairo
PublicationPlace_xml – name: Cairo
PublicationTitle Journal of Mathematics
PublicationYear 2022
Publisher Hindawi
John Wiley & Sons, Inc
Wiley
Publisher_xml – name: Hindawi
– name: John Wiley & Sons, Inc
– name: Wiley
References Peter T. (e_1_2_8_9_2) 2013
e_1_2_8_27_2
e_1_2_8_28_2
e_1_2_8_29_2
e_1_2_8_24_2
e_1_2_8_25_2
e_1_2_8_26_2
Birkhoff G. (e_1_2_8_23_2) 1982
e_1_2_8_2_2
e_1_2_8_1_2
e_1_2_8_4_2
e_1_2_8_3_2
e_1_2_8_6_2
e_1_2_8_5_2
e_1_2_8_8_2
e_1_2_8_7_2
e_1_2_8_20_2
e_1_2_8_21_2
Hale J. K. (e_1_2_8_22_2) 2013; 99
e_1_2_8_17_2
e_1_2_8_18_2
e_1_2_8_19_2
e_1_2_8_12_2
e_1_2_8_13_2
Yang K. (e_1_2_8_16_2) 2012
e_1_2_8_14_2
e_1_2_8_15_2
e_1_2_8_10_2
e_1_2_8_11_2
References_xml – ident: e_1_2_8_13_2
  doi: 10.1142/s1793524518500109
– ident: e_1_2_8_14_2
  doi: 10.1186/s13662-020-02579-z
– ident: e_1_2_8_8_2
  doi: 10.1007/b98868
– ident: e_1_2_8_24_2
  doi: 10.1016/s0960-0779(02)00079-6
– ident: e_1_2_8_2_2
  doi: 10.1186/s13662-021-03490-x
– volume-title: Complex Population Dynamics
  year: 2013
  ident: e_1_2_8_9_2
– ident: e_1_2_8_27_2
  doi: 10.1016/j.ecocom.2015.12.001
– ident: e_1_2_8_15_2
  doi: 10.1155/2020/7306412
– ident: e_1_2_8_26_2
  doi: 10.3934/mbe.2019121
– ident: e_1_2_8_28_2
  doi: 10.1142/s1793524522500140
– ident: e_1_2_8_17_2
  doi: 10.1007/978-981-16-0626-7
– ident: e_1_2_8_3_2
  doi: 10.1186/s13662-021-03216-z
– ident: e_1_2_8_29_2
  doi: 10.1007/s11071-016-2844-8
– year: 1982
  ident: e_1_2_8_23_2
  article-title: Ordinray Differential Equations
  publication-title: Ginn Boston
– ident: e_1_2_8_19_2
  doi: 10.1016/j.ecocom.2014.01.004
– ident: e_1_2_8_4_2
  doi: 10.1155/2022/6931354
– ident: e_1_2_8_11_2
  doi: 10.1098/rspb.2003.2555
– volume-title: Delay Differential Equations
  year: 2012
  ident: e_1_2_8_16_2
– ident: e_1_2_8_7_2
  doi: 10.1016/j.amc.2020.125919
– ident: e_1_2_8_18_2
  doi: 10.3934/dcdss.2020468
– ident: e_1_2_8_20_2
  doi: 10.1016/j.chaos.2021.111212
– ident: e_1_2_8_21_2
  doi: 10.1007/s12555-020-0526-2
– ident: e_1_2_8_6_2
  doi: 10.1186/s13662-020-02609-w
– ident: e_1_2_8_25_2
  doi: 10.1142/s0218127415501230
– ident: e_1_2_8_10_2
  doi: 10.1086/282272
– ident: e_1_2_8_12_2
  doi: 10.1007/s00285-005-0342-6
– ident: e_1_2_8_1_2
  doi: 10.1016/j.amc.2019.03.034
– ident: e_1_2_8_5_2
  doi: 10.1186/s13662-019-2289-8
– volume: 99
  year: 2013
  ident: e_1_2_8_22_2
  article-title: Introduction to functional differential equations
  publication-title: Springer Science & Business Media
SSID ssj0001283890
ssib026596782
ssib050733809
Score 2.2423956
Snippet In this article, we propose the Holling type-II predator-prey model involving cannibalism and gestation delay in predators. We study the existence of all...
In this article, we propose the Holling type‐II predator‐prey model involving cannibalism and gestation delay in predators. We study the existence of all...
SourceID doaj
proquest
gale
crossref
hindawi
SourceType Open Website
Aggregation Database
Enrichment Source
Index Database
Publisher
SubjectTerms Cannibalism
Endangered & extinct species
Equilibrium
Extinction
Hopf bifurcation
Mathematics
Population
Predator-prey simulation
Predators
Stability analysis
SummonAdditionalLinks – databaseName: DOAJ Directory of Open Access Journals
  dbid: DOA
  link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV3fa9swEBajMOgeSrduNGta9JDShyGaWLrYfuyvkBQy-rBCX4aQdTItpGlJM0r_-95ZikkZoy97MNjWgaXTSXffIX8nRI-iUB1qr5WvC1Am74Mqc-0UAIbAbC4xmTP9ORxfm8sbuFkr9cVnwiI9cFTccTBQgtd5URXGgCPv5CHjs4kVaDK-BviQz1sDUzG7UpAn7q9OugMwyM-OGb1oPlK45oMaqv52Q_54y1D4-e6vrbnxN6NtsZUCRXkSO_hZfAjzL-LTtGVZfdoRv89jOXkSSzSHC_lQSyfPw8y9BJTjyLgtGWyqyUReLQIyyFZ08yK5DNpMciK2bZBnXMKoYlLE-6_ienTx62ysUrkE5UnHS4UAGepgNEVVJWKNwdeG6d585Ycur8PAOXAI6EtToSE_PvBYFmhc5o2nx29iY_4wD7tCFsisPgbocgbBVY4CyQrzUODQuCF2xI-VAq1PXOJc0mJmG0wBYFndNqm7Iw5b6cfIofEPuVOei1aGma-bF2QPNtmDfc8eOuKIZ9Ly-qQueZd-M6CBMdOVPSm0piinn2cd0X0jSevKv2nuJVt4p9PdlaHYtPyfbEYgGQY5hcvf_8eY9sQmfzJmfrpiY7n4E_YpFlpWB43ZvwLi8v5B
  priority: 102
  providerName: Directory of Open Access Journals
– databaseName: Hindawi Publishing Open Access
  dbid: RHX
  link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV3da9swEBdrYdA-lH2VZsuGHlr6MERjS-ePx6xdSQcdfWghL0PIOpkW0nQkKSP__e5s2SwrZXswWNYh5NOd7sPy74Q4JC9Uh9pr5esClMlHoMpcOwWAITCaS5vMufyeTW7MtylMI0jS8uknfLJ2HJ6nJxx36By2xBYJGAflk2knNmkGZfYHKDtwHcIOlapNtRRklkdNmbnEKJOlZXcE_q_hN4xTg-Hf79QvbzlG_nX3ZM9uDNH5K7EXPUg5bpf8tXgR5m_E7mUPv7p8K36ctXXmiSziHy7kQy2dPAsztw4oJy0Ut-QoVF1cyKtFQI6-Fd2sJddHm0nO0PYd8pRrG1WMlnj_Ttycf70-nahYR0F5Yv5KIUCKOhhN7laJWGPwtWEcOF_5zOV1SJwDh4C-NBUaMvCJx7JA41JvPDX3xfb8YR4OhCyQ4X4M0OUMgqsceZgV5qHAzLgMB-Jzx0DrI8g417qY2SbYALDMbhvZPRBHPfXPFlzjGbovvBY9DUNiNw9ITGzUMBsMlOB1XlSFMeDIjfGQ8iHWCjTtUslAHPNKWlZcmpJ38f8DejGGwLLjQmtyf0Z5OhDDDUpSOL_RfRhl4R-THnaCYuO-sLQpRc-Q5ORHv_-_UT6IHW62SZ-h2F4tHsNHcoNW1adGCX4DO372nQ
  priority: 102
  providerName: Hindawi Publishing
Title Dynamical Behavior of a Delayed Holling Type-II Predator-Prey Model with Predator Cannibalism
URI https://dx.doi.org/10.1155/2022/4071375
https://www.proquest.com/docview/2717517045
https://doaj.org/article/e4595c378b8445a293c524105b534881
Volume 2022
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwhV3db9MwELfYJiR4mPjUykrlhyEekLUm9iXOE9pHS4fUaZqY1BdkObYDk0o72iK0F_527hInMCHgIVYSnyLHPp_vLs7vx9gBeqEyVE4KV2kQKh-CKHJpBYAPgdBcmmTO9DybXKn3M5jFhNs6bqtsbWJtqP3SUY78MMW4A5IcPZC3N18FsUbR19VIobHFdtAEawy-do5H5xeXrUYBURK2AFVN1kXjCj2sGecSJVSWFu1ueABKBKSHFOFI2nb42zpVw_l3Rvv-ZwqXv1__Yb7rNWn8iO1GZ5IfNaP_mN0Liyfs4bRDYl0_ZR9PG8p5FItQiCu-rLjlp2Fub4PnkwaVm1NAKs7O-MUqeArEBZ7ccqJKm3NK1nYV_IRojkoCTvzyjF2NRx9OJiJSKgiH47ARHiD1MiiJnlfhfeWDqxRBwrnSZTavQmItWA_eFar0Ctf6xPlCe2VTpxxePmfbi-Ui7DGuPSH_KMDDKg-2tOhslj4P2mfKZr7H3rQdaFzEGyfai7mp4w4AQ91tYnf32KtO-qbB2fiL3DGNRSdD6Nj1jeXqk4mTzQQFBTiZ61IrBRY9Ggcp7WctQaLBSnrsNY2koTmMTXI2_oqAL0ZoWOZIS4me0DBPe6x_RxLnnrtTfRB14T-N7reKYqKJWJtfCv3i39X77AE9rMn79Nn2ZvUtvERPaFMO2JYevxtEpR_U-QQspz9GWF5OZj8BQqkC1w
linkProvider ProQuest
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1LbxMxELZKEaIcEE8RCOBDKw7Ianbtye4eECoNIaFNxaGVekHG6_FSpJCUJKjKn-I3MrMvqBBw6mGlbDxaOfa84_0-IbYpC9Wh8Fr5IgVlkh6oLNFOAWAIjOZSNXMmR_3RiXl_Cqcb4kfzLgwfq2x8Yumoce65R74bU90BUUIZyOvzb4pZo_jf1YZCo1KLg7C-oJJt-Wo8oP3diePh2-P9kapZBZSnqawUAsSog9GUfGSIBQZfGEZF87nvu6QIkXPgENBnJkdD4S7ymKVoXOyNp1t67jVx3WidsUWlw3eN_gITIDZwWFWPJ6V8oFfy20VGmX6cNWfvAbjtEO9yPaX5kONvUbEkD2hDxI0zLs4vvvwRLMoIOLwjbtepq9yrdO2u2Aize-LWpMV9Xd4XHwcVwT2J1cCLCzkvpJODMHXrgHJUYYBLLn_VeCw_LAJy2a_ow1oyMdtUcmu4HZD7TKqUM0zj1wfi5EqW-qHYnM1n4ZGQKTLOkAG6nEFwuaPUNsckpNg3ro8d8bJZQOtrdHMm2ZjassoBsLzctl7ujthppc8rVI-_yL3hvWhlGIu7_GK--Gxr07bBQAZeJ2meGgOO8icPMZ-ezUGTe4w64gXvpGWPQVPyrn7xgX4YY2_ZvVRryrt6SdwR3UuSZOn-0vB2rQv_mXS3URRbO6Sl_WU-j_89_FzcHB1PDu3h-OjgidjiB1cdp67YXC2-h6eUg63yZ6XiS_Hpqi3tJ-A4PD4
linkToPdf http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1LbxMxELZKKlA5IJ4iEMCHVhyQlezas48DQm3TKKE0ihCVekHGa3spUkhKElTlr_HrmNn1BioEnHpYKRuPVo49M56ZzH4fY7sYhUpfWilsmYFQaQ9EnkojAJz3hOZSF3NOxsnwVL09g7Mt9qN5F4baKhufWDlqN7dUI-_GmHdAlGIE0i1DW8SkP3hz8U0QgxT909rQadQqcuzXl5i-LV-P-rjXe3E8OPpwOBSBYUBYnNZKOIDYSa8kBiK5c6XztlSEkGYLm5i09JExYBw4m6vCKTz6IuvyzCkTW2XxFp97g22nmBX1Wmz74Gg8ed9oMxAdYgOOVVd8MowOehXbXaSESuK86cQHoCJE3KXsSlLL429nZEUlsDkwbp5Tqn755Y-jozoPB3fZnRDI8v1a8-6xLT-7z26fbFBglw_Yx35Nd49iAYZxweclN7zvp2btHR_WiOCckmExGvHJwjsqAgj8sOZE0zblVCjeDPBDolgqCLTx60N2ei2L_Yi1ZvOZf8x45gh1SAFeRjkwhcFAt3Cpz1yiTOLa7FWzgNoGrHOi3JjqKucB0LTcOix3m-1tpC9qjI-_yB3QXmxkCJm7-mK--KyDoWuvIAcr06zIlAKD0ZSFmHppC5DoLKM2e0k7qcl_4JSsCa9B4A8jJC69n0mJUVgvjdusc0US7d5eGd4NuvCfSXcaRdHBPS31L2N68u_hF-wWWpl-NxofP2U79Ny6_NRhrdXiu3-GAdmqeB40n7NP121sPwFEOUHQ
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=Dynamical+Behavior+of+a+Delayed+Holling+Type-II+Predator-Prey+Model+with+Predator+Cannibalism&rft.jtitle=Journal+of+Mathematics&rft.au=Lavanya%2C+R&rft.au=Vinoth%2C+S&rft.au=Sathiyanathan%2C+K&rft.au=Njitacke+Tabekoueng%2C+Zeric&rft.date=2022&rft.pub=John+Wiley+%26+Sons%2C+Inc&rft.issn=2314-4629&rft.volume=2022&rft_id=info:doi/10.1155%2F2022%2F4071375&rft.externalDocID=A833151072
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2314-4629&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2314-4629&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2314-4629&client=summon