A Novel Discrete-Time Leslie–Gower Model with the Impact of Allee Effect in Predator Population

The discrete-time system has more complex and chaotic dynamical behaviors as compared to the continuous-time system. This paper extends a discrete Leslie–Gower predator-prey system with the Allee effect in the predator’s population, whose dynamics are analyzed and explored. We have determined the eq...

Full description

Saved in:
Bibliographic Details
Published inComplexity (New York, N.Y.) Vol. 2022; no. 1
Main Authors Vinoth, S., Sivasamy, R., Sathiyanathan, K., Unyong, B., Vadivel, R., Gunasekaran, Nallappan
Format Journal Article
LanguageEnglish
Published Hoboken Hindawi 2022
John Wiley & Sons, Inc
Wiley
Subjects
Behavior
Bifurcation theory
Canonical forms
Comparative analysis
Continuous time systems
Control methods
Discrete systems
Discrete time systems
Equilibrium
Hybrid control
Mathematical models
Numerical analysis
Parameters
Pole placement
Population
Predator-prey simulation
Predators
Simulation methods
Stability
State feedback
Germany
Online AccessGet full text

Cover

Abstract The discrete-time system has more complex and chaotic dynamical behaviors as compared to the continuous-time system. This paper extends a discrete Leslie–Gower predator-prey system with the Allee effect in the predator’s population, whose dynamics are analyzed and explored. We have determined the equilibrium points and studied their local stability properties. We find that the system undergoes flip bifurcation and Neimark–Sacker bifurcation around the interior equilibrium point by choosing the Allee parameter as a bifurcation parameter. We discuss the stability and direction of both bifurcations with the help of the normal form theory and center manifold theorem. The flip bifurcation and Neimark–Sacker bifurcation are the most common routes to the chaotic orbit in the discrete system. Moreover, we utilize state feedback, pole placement, and hybrid control methods to control the chaos in the system. The work is complete with the numerical simulations to confirm the analytical findings.
AbstractList The discrete-time system has more complex and chaotic dynamical behaviors as compared to the continuous-time system. This paper extends a discrete Leslie–Gower predator-prey system with the Allee effect in the predator’s population, whose dynamics are analyzed and explored. We have determined the equilibrium points and studied their local stability properties. We find that the system undergoes flip bifurcation and Neimark–Sacker bifurcation around the interior equilibrium point by choosing the Allee parameter as a bifurcation parameter. We discuss the stability and direction of both bifurcations with the help of the normal form theory and center manifold theorem. The flip bifurcation and Neimark–Sacker bifurcation are the most common routes to the chaotic orbit in the discrete system. Moreover, we utilize state feedback, pole placement, and hybrid control methods to control the chaos in the system. The work is complete with the numerical simulations to confirm the analytical findings.
Audience Academic
Author Vadivel, R.
Unyong, B.
Sathiyanathan, K.
Sivasamy, R.
Vinoth, S.
Gunasekaran, Nallappan
Author_xml – sequence: 1
  givenname: S.
  orcidid: 0000-0002-4509-9484
  surname: Vinoth
  fullname: Vinoth, S.
  organization: Department of MathematicsSRMV College of Arts and ScienceCoimbatoreTNIndia
– sequence: 2
  givenname: R.
  orcidid: 0000-0002-9784-2591
  surname: Sivasamy
  fullname: Sivasamy, R.
  organization: Department of Science and HumanitiesM.Kumarasamy College of EngineeringKarurTNIndiamkce.ac.in
– sequence: 3
  givenname: K.
  orcidid: 0000-0002-3994-3896
  surname: Sathiyanathan
  fullname: Sathiyanathan, K.
  organization: Department of MathematicsSRMV College of Arts and ScienceCoimbatoreTNIndia
– sequence: 4
  givenname: B.
  orcidid: 0000-0002-8832-3036
  surname: Unyong
  fullname: Unyong, B.
  organization: Department of MathematicsFaculty of Science and TechnologyPhuket Rajabhat UniversityPhuket 83000Thailandpkru.ac.th
– sequence: 5
  givenname: R.
  orcidid: 0000-0002-1385-5345
  surname: Vadivel
  fullname: Vadivel, R.
  organization: Department of MathematicsFaculty of Science and TechnologyPhuket Rajabhat UniversityPhuket 83000Thailandpkru.ac.th
– sequence: 6
  givenname: Nallappan
  orcidid: 0000-0003-0375-7917
  surname: Gunasekaran
  fullname: Gunasekaran, Nallappan
  organization: Department of Advanced Science and TechnologyComputational Intelligence LaboratoryToyota Technological InstituteNagoya 468-8511Japantoyota-ti.ac.jp
BookMark eNp9UctuEzEUHaEi0RZ2fIAlljCt32Mvo1JKpABdlLXlsa8bR5Nx8DhE7PiH_mG_BKepKoEAeWHfq3POvT7npDka0whN85rgM0KEOKeY0nOpGWGCP2uOCda6xYLKo_27ky3tVPeiOZmmFcZYS9YdN3aGPqfvMKD3cXIZCrQ3cQ1oAdMQ4f7n3VXaQUafkq-QXSxLVJaA5uuNdQWlgGbDAIAuQ4BaxxFdZ_C2pIyu02Y72BLT-LJ5HuwwwavH-7T5-uHy5uJju_hyNb-YLVrHO1xawSSrMr2wrldScx0UBGw9E8CCD94CIZ3vSU-1xMAh9IFjyrQPUgF2mp0284OuT3ZlNjmubf5hko3moZHyrbG5RDeA4UIJBVYE3ncceqsdo5Ypz4lyinhftd4ctDY5fdvCVMwqbfNY1zdUcqWqm3XdJ9StraJxDKlk69bVSDNTjHIhmSIVdfYXVD0e1tHVAEOs_d8I7w4El9M0ZQhPnyHY7HM2-5zNY84VTv-Au1genK9z4vAv0tsDaRlHb3fx_yN-AXN7uFM
CitedBy_id crossref_primary_10_1155_2023_5030729
crossref_primary_10_1155_2023_5537632
crossref_primary_10_1007_s40995_024_01665_1
crossref_primary_10_1142_S0218127422501723
crossref_primary_10_3390_fractalfract7080570
crossref_primary_10_1088_1402_4896_ad848a
crossref_primary_10_1155_2024_9185585
crossref_primary_10_1016_j_cnsns_2024_108477
crossref_primary_10_1155_2023_4555469
crossref_primary_10_1142_S0217984925501039
crossref_primary_10_1142_S0218127424500147
crossref_primary_10_1155_2024_9912671
crossref_primary_10_1186_s13661_023_01770_x
crossref_primary_10_3934_math_20231165
crossref_primary_10_1155_2022_4071375
crossref_primary_10_3390_axioms12060561
Cites_doi 10.1016/j.ecocom.2010.04.005
10.1016/j.cnsns.2017.01.025
10.1016/j.chaos.2007.09.077
10.1007/s11071-015-1927-2
10.1142/3033
10.1186/s13662-019-2319-6
10.1016/j.jmaa.2010.11.008
10.1142/s0218127415300074
10.1007/978-3-319-78145-7
10.1186/s13662-021-03216-z
10.5962/bhl.title.7313
10.1016/j.chaos.2005.03.040
10.1016/j.ecocom.2012.01.002
10.1080/10236198.2020.1739276
10.1109/access.2020.3030778
10.1051/mmnp/2020042
10.1186/s13662-015-0546-z
10.1186/s13662-020-2498-1
10.1016/j.nonrwa.2007.08.029
10.1126/science.186.4164.645
10.1016/s0168-9274(02)00223-4
10.1177/1077546318790871
10.1142/S179352451950044X
10.1016/j.amc.2014.12.021
10.1201/9781482227871
10.1016/j.jmaa.2009.05.039
10.1186/s13662-021-03490-x
10.1139/f54-039
10.1103/physrevlett.64.1196
10.1186/s13662-019-1950-6
10.1016/s0893-9659(03)90096-6
10.1016/j.cnsns.2016.02.038
10.1016/j.nonrwa.2010.06.026
10.1142/s0218127418500839
10.1023/a:1004918920121
10.1142/6882
10.1016/j.chaos.2005.10.081
10.1016/j.apm.2014.10.040
ContentType Journal Article
Copyright Copyright © 2022 S. Vinoth et al.
COPYRIGHT 2022 John Wiley & Sons, Inc.
Copyright © 2022 S. Vinoth 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 S. Vinoth et al.
– notice: COPYRIGHT 2022 John Wiley & Sons, Inc.
– notice: Copyright © 2022 S. Vinoth 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.
7XB
8FE
8FG
8FK
8G5
ABUWG
AFKRA
ARAPS
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
GNUQQ
GUQSH
HCIFZ
JQ2
K7-
M2O
MBDVC
P5Z
P62
PHGZM
PHGZT
PKEHL
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
Q9U
DOA
DOI 10.1155/2022/6931354
DatabaseName Hindawi Publishing Complete
Hindawi Publishing Subscription Journals
Hindawi Publishing Open Access
CrossRef
ProQuest Central (Corporate)
ProQuest Central (purchase pre-March 2016)
ProQuest SciTech Collection
ProQuest Technology Collection
ProQuest Central (Alumni) (purchase pre-March 2016)
ProQuest Research Library
ProQuest Central (Alumni)
ProQuest Central UK/Ireland
Advanced Technologies & Aerospace Collection
ProQuest Central Essentials
ProQuest Central
Technology Collection
ProQuest One
ProQuest Central
ProQuest Central Student
ProQuest Research Library
SciTech Premium Collection
ProQuest Computer Science Collection
Computer Science Database
Research Library
Research Library (Corporate)
ProQuest advanced technologies & aerospace journals
ProQuest Advanced Technologies & Aerospace Collection
ProQuest Central Premium
ProQuest One Academic (New)
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
ProQuest Central Basic
DOAJ Directory of Open Access Journals
DatabaseTitle CrossRef
Research Library Prep
Computer Science Database
ProQuest Central Student
Technology Collection
ProQuest One Academic Middle East (New)
ProQuest Advanced Technologies & Aerospace Collection
ProQuest Central Essentials
ProQuest Computer Science Collection
ProQuest Central (Alumni Edition)
SciTech Premium Collection
ProQuest One Community College
Research Library (Alumni Edition)
ProQuest Central China
ProQuest Central
ProQuest One Applied & Life Sciences
ProQuest Central Korea
ProQuest Research Library
ProQuest Central (New)
Advanced Technologies & Aerospace Collection
ProQuest Central Basic
ProQuest One Academic Eastern Edition
ProQuest Technology Collection
ProQuest SciTech Collection
Advanced Technologies & Aerospace Database
ProQuest One Academic UKI Edition
ProQuest One Academic
ProQuest One Academic (New)
ProQuest Central (Alumni)
DatabaseTitleList Research Library Prep


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 Sciences (General)
Mathematics
EISSN 1099-0526
Editor Rajivganthi, C.
Editor_xml – sequence: 1
  givenname: C.
  surname: Rajivganthi
  fullname: Rajivganthi, C.
ExternalDocumentID oai_doaj_org_article_45858ea5f4b74eba9c32a38d418c81dd
A832456381
10_1155_2022_6931354
GeographicLocations Germany
GeographicLocations_xml – name: Germany
GroupedDBID .3N
.DC
.GA
05W
0R~
10A
1L6
24P
3SF
3WU
4.4
4ZD
50Y
50Z
51W
51X
52M
52N
52O
52P
52S
52T
52U
52W
52X
5GY
66C
702
7PT
8-0
8-1
8-3
8-4
8-5
8FE
8FG
8G5
8UM
930
A03
AAESR
AAFWJ
AAJEY
AAONW
ABCQN
ABEML
ABIJN
ABPVW
ABUWG
ACCMX
ACSCC
ADBBV
ADIZJ
AENEX
AFBPY
AFKRA
AFPKN
AJXKR
ALAGY
ALMA_UNASSIGNED_HOLDINGS
AMBMR
ARAPS
ATUGU
AZBYB
AZQEC
AZVAB
BAFTC
BCNDV
BENPR
BGLVJ
BHBCM
BNHUX
BPHCQ
BROTX
BRXPI
BY8
CCPQU
CS3
D-E
D-F
DPXWK
DR2
DU5
DWQXO
EBD
EBS
F00
F01
F04
F5P
G-S
G.N
GNP
GNUQQ
GODZA
GROUPED_DOAJ
GUQSH
H.T
H.X
H13
HBH
HCIFZ
HHY
HZ~
IAO
ICD
ITC
IX1
J0M
JPC
K6V
K7-
KQQ
LAW
LC2
LC3
LP6
LP7
M2O
MK4
N04
N05
N9A
NF~
NNB
O9-
OIG
OK1
P2P
P2X
P4D
P62
PHGZT
PQQKQ
PROAC
Q.N
Q11
QB0
QRW
R.K
RHU
RHW
RHX
RX1
RYL
SUPJJ
TUS
V2E
W8V
W99
WBKPD
WQJ
XG1
XPP
XSW
XV2
~IA
~WT
.Y3
31~
3R3
5VS
AAEVG
AAHHS
AANHP
AAYXX
ACBWZ
ACCFJ
ACRPL
ACXQS
ACYXJ
ADNMO
ADZOD
AEEZP
AEIMD
AEQDE
AFZJQ
AGQPQ
AIWBW
AJBDE
AMVHM
ASPBG
AVWKF
AZFZN
BDRZF
BFHJK
CITATION
DCZOG
EJD
FEDTE
HF~
HVGLF
LH4
LW6
PHGZM
ROL
WYUIH
PMFND
3V.
7XB
8FK
AAMMB
AEFGJ
AGXDD
AIDQK
AIDYY
JQ2
MBDVC
PKEHL
PQEST
PQGLB
PQUKI
PRINS
Q9U
PUEGO
ID FETCH-LOGICAL-c470t-5363ffeb5acb86949f8ef0ad35e3fdfdae117db1b2960e4efbf40239df68e0c93
IEDL.DBID BENPR
ISSN 1076-2787
IngestDate Wed Aug 27 01:31:16 EDT 2025
Fri Jul 25 20:59:45 EDT 2025
Tue Jun 17 21:58:42 EDT 2025
Tue Jun 10 21:01:45 EDT 2025
Thu Apr 24 23:03:06 EDT 2025
Tue Jul 01 02:08:25 EDT 2025
Wed Apr 16 06:22:53 EDT 2025
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-5363ffeb5acb86949f8ef0ad35e3fdfdae117db1b2960e4efbf40239df68e0c93
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0000-0002-9784-2591
0000-0002-3994-3896
0000-0002-4509-9484
0000-0002-1385-5345
0000-0002-8832-3036
0000-0003-0375-7917
OpenAccessLink https://dx.doi.org/10.1155/2022/6931354
PQID 2648810736
PQPubID 2029978
ParticipantIDs doaj_primary_oai_doaj_org_article_45858ea5f4b74eba9c32a38d418c81dd
proquest_journals_2648810736
gale_infotracmisc_A832456381
gale_infotracacademiconefile_A832456381
crossref_primary_10_1155_2022_6931354
crossref_citationtrail_10_1155_2022_6931354
hindawi_primary_10_1155_2022_6931354
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2022-00-00
PublicationDateYYYYMMDD 2022-01-01
PublicationDate_xml – year: 2022
  text: 2022-00-00
PublicationDecade 2020
PublicationPlace Hoboken
PublicationPlace_xml – name: Hoboken
PublicationTitle Complexity (New York, N.Y.)
PublicationYear 2022
Publisher Hindawi
John Wiley & Sons, Inc
Wiley
Publisher_xml – name: Hindawi
– name: John Wiley & Sons, Inc
– name: Wiley
References e_1_2_11_31_2
e_1_2_11_30_2
Freedman H. I. (e_1_2_11_3_2) 1980
e_1_2_11_13_2
e_1_2_11_35_2
e_1_2_11_12_2
e_1_2_11_34_2
e_1_2_11_11_2
e_1_2_11_33_2
e_1_2_11_10_2
e_1_2_11_32_2
e_1_2_11_5_2
e_1_2_11_27_2
e_1_2_11_4_2
e_1_2_11_26_2
e_1_2_11_25_2
e_1_2_11_2_2
e_1_2_11_1_2
Kuznetsov Y. A. (e_1_2_11_28_2) 2013
e_1_2_11_29_2
Murray J. D. (e_1_2_11_17_2) 2002
e_1_2_11_20_2
e_1_2_11_43_2
e_1_2_11_24_2
e_1_2_11_9_2
e_1_2_11_23_2
e_1_2_11_40_2
e_1_2_11_8_2
e_1_2_11_22_2
e_1_2_11_41_2
e_1_2_11_7_2
e_1_2_11_21_2
Guckenheimer J. (e_1_2_11_42_2) 2013
e_1_2_11_16_2
e_1_2_11_15_2
e_1_2_11_14_2
e_1_2_11_36_2
e_1_2_11_37_2
e_1_2_11_19_2
e_1_2_11_38_2
e_1_2_11_18_2
e_1_2_11_39_2
Elalim A. (e_1_2_11_6_2) 2012; 2
References_xml – ident: e_1_2_11_24_2
  doi: 10.1016/j.ecocom.2010.04.005
– ident: e_1_2_11_32_2
  doi: 10.1016/j.cnsns.2017.01.025
– ident: e_1_2_11_23_2
  doi: 10.1016/j.chaos.2007.09.077
– ident: e_1_2_11_20_2
  doi: 10.1007/s11071-015-1927-2
– ident: e_1_2_11_27_2
  doi: 10.1142/3033
– ident: e_1_2_11_8_2
  doi: 10.1186/s13662-019-2319-6
– ident: e_1_2_11_38_2
  doi: 10.1016/j.jmaa.2010.11.008
– ident: e_1_2_11_21_2
  doi: 10.1142/s0218127415300074
– ident: e_1_2_11_30_2
  doi: 10.1007/978-3-319-78145-7
– ident: e_1_2_11_22_2
  doi: 10.1186/s13662-021-03216-z
– volume-title: Deterministic Mathematical Models in Population Ecology
  year: 1980
  ident: e_1_2_11_3_2
– ident: e_1_2_11_18_2
  doi: 10.5962/bhl.title.7313
– ident: e_1_2_11_4_2
  doi: 10.1016/j.chaos.2005.03.040
– ident: e_1_2_11_19_2
  doi: 10.1016/j.ecocom.2012.01.002
– ident: e_1_2_11_26_2
  doi: 10.1080/10236198.2020.1739276
– ident: e_1_2_11_35_2
  doi: 10.1109/access.2020.3030778
– ident: e_1_2_11_33_2
  doi: 10.1051/mmnp/2020042
– ident: e_1_2_11_39_2
  doi: 10.1186/s13662-015-0546-z
– volume-title: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector fields
  year: 2013
  ident: e_1_2_11_42_2
– ident: e_1_2_11_34_2
  doi: 10.1186/s13662-020-2498-1
– volume: 2
  year: 2012
  ident: e_1_2_11_6_2
  article-title: Chaos and bifurcation of a nonlinear discrete prey-predator system
  publication-title: Computational Ecology and Software
– ident: e_1_2_11_15_2
  doi: 10.1016/j.nonrwa.2007.08.029
– ident: e_1_2_11_2_2
  doi: 10.1126/science.186.4164.645
– ident: e_1_2_11_9_2
  doi: 10.1016/s0168-9274(02)00223-4
– ident: e_1_2_11_11_2
  doi: 10.1177/1077546318790871
– ident: e_1_2_11_12_2
  doi: 10.1142/S179352451950044X
– ident: e_1_2_11_13_2
  doi: 10.1016/j.amc.2014.12.021
– ident: e_1_2_11_43_2
  doi: 10.1201/9781482227871
– ident: e_1_2_11_37_2
  doi: 10.1016/j.jmaa.2009.05.039
– ident: e_1_2_11_41_2
  doi: 10.1186/s13662-021-03490-x
– volume-title: Mathematicalbiology I. An Introduction
  year: 2002
  ident: e_1_2_11_17_2
– ident: e_1_2_11_16_2
  doi: 10.1139/f54-039
– ident: e_1_2_11_31_2
  doi: 10.1103/physrevlett.64.1196
– ident: e_1_2_11_40_2
  doi: 10.1186/s13662-019-1950-6
– ident: e_1_2_11_36_2
  doi: 10.1016/s0893-9659(03)90096-6
– ident: e_1_2_11_25_2
  doi: 10.1016/j.cnsns.2016.02.038
– ident: e_1_2_11_7_2
  doi: 10.1016/j.nonrwa.2010.06.026
– ident: e_1_2_11_14_2
  doi: 10.1142/s0218127418500839
– ident: e_1_2_11_1_2
  doi: 10.1023/a:1004918920121
– volume-title: Elements of Applied Bifurcation Theory
  year: 2013
  ident: e_1_2_11_28_2
– ident: e_1_2_11_10_2
  doi: 10.1142/6882
– ident: e_1_2_11_5_2
  doi: 10.1016/j.chaos.2005.10.081
– ident: e_1_2_11_29_2
  doi: 10.1016/j.apm.2014.10.040
SSID ssj0009637
Score 2.347231
Snippet The discrete-time system has more complex and chaotic dynamical behaviors as compared to the continuous-time system. This paper extends a discrete Leslie–Gower...
The discrete‐time system has more complex and chaotic dynamical behaviors as compared to the continuous‐time system. This paper extends a discrete Leslie–Gower...
The discrete-time system has more complex and chaotic dynamical behaviors as compared to the continuous-time system. This paper extends a discrete Leslie-Gower...
SourceID doaj
proquest
gale
crossref
hindawi
SourceType Open Website
Aggregation Database
Enrichment Source
Index Database
Publisher
SubjectTerms Behavior
Bifurcation theory
Canonical forms
Comparative analysis
Continuous time systems
Control methods
Discrete systems
Discrete time systems
Equilibrium
Hybrid control
Mathematical models
Numerical analysis
Parameters
Pole placement
Population
Predator-prey simulation
Predators
Simulation methods
Stability
State feedback
SummonAdditionalLinks – databaseName: DOAJ Directory of Open Access Journals
  dbid: DOA
  link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1Lb9QwELZQJSQ4IFpALCzIhyJAKGq8thPnuDxKQbTqgUq9WX6M1ZWiXdTdliv_gX_IL2EmcSJWCPXCNXES2_PwN47nG8b2tQupKr0vhGlMoRoIaHPQFHVAVxi1rJyjfcjjk-roTH0-1-d_lPqiM2E9PXA_cQcK8awBp5PytQLvmiBnTpqohAmItSJ5X1zzhmBqoNutZD0cc9eaIvzZQdVIIbXaWoA6nv7RG9--oDj4--Ivv9wtNof32b2MEvm8790uuwXLPXb3eKRYXe-x3WyVa_4qU0e_fsDcnJ-srqHl7xfoDhAPF5Tiwb8Aokn49ePnR6qJxqn-WctpB5bjC_mnLlGSrxKfty0A7wmN-WLJTy8hUlDOT8cyXw_Z2eGHr--OilxEoQiqLjcFTrfExzwKxZuqUU0ykEoXpQaZYooOhKijF36GsQwoSD4pSniNqTJQhkY-YjvL1RIeMy58qOm3axC1VLOE0BJEkkKAK51KpZywN8PM2pAZxqnQRWu7SENrS3KwWQ4T9mJs_a1n1vhHu7ckpLEN8WF3F1BLbNYSe5OWTNhLErElq8UuBZeTD3BgxH9l5-jYEEoifJmw6VZLtLawdXs_K8kNnZ4OGmSzU1hbOkxoMNyW1ZP_Maan7A59st8PmrKdzeUVPEOEtPHPO2P4DfyHCt4
  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/eLvHCXMwjV1Lj9MwELbYlZDggNgFRKEgHxYBQhFx7DjOsTyWgtjVHlipN8uPsbZS1KJtgSv_gX_IL2EmdYPKCsExydhyPA_P2J5vGDuqXUi69L4QpjWFaiGgzkFbNAFNYayldo72IU9O9fRcfZjVswyStLp6hI-rHYXn1UvdSiFrtcf2UMAoKJ_OfmPr6h4aEwMZXVQogNv77X-03Vl5eoD-wQxfv6AA-Nv8ikHuV5nj2-xWdg_5ZMPPA3YNFofs5smArbo6ZAdZHVf8WcaMfn6HuQk_XX6Fjr-Zox1AR7ig3A7-EdCNhJ_ff7yjYmicCp91nLZeOXbI3_cZknyZ-KTrAPgGyZjPF_zsEiJF4_xsqO91l50fv_30elrk6glFUE25LnCeJTbzyA1vdKvaZCCVLsoaZIopOhCiiV74CoMYUJB8UpTpGpM2UIZW3mP7i-UC7jMufGjovDWIRqoqoU8JIkkhwJVOpVKO2IvtzNqQocWpwkVn-xCjri3xwWY-jNiTgfrzBlLjL3SviEkDDQFh9y9QOGzWK6sw3DHg6qR8o8C7NsjKSROVMAFd8ThiT4nFltQVhxRczjrAHyPgKztBi4Y-JPotIzbeoUQ1Czufj7KQ_GPQ460E2WwNVpZuERoUT6kf_F8vD9kNetxs9YzZ_vryCzxC52ftH_ei_wsqtflk
  priority: 102
  providerName: Hindawi Publishing
Title A Novel Discrete-Time Leslie–Gower Model with the Impact of Allee Effect in Predator Population
URI https://dx.doi.org/10.1155/2022/6931354
https://www.proquest.com/docview/2648810736
https://doaj.org/article/45858ea5f4b74eba9c32a38d418c81dd
Volume 2022
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwhV1Rb9MwELbYJiR4QGyA1lEqPwwBQtHi2EmcJ9TBuoJYVU1M6ltkO2eoVDWj7eCV_8A_5Jdwl7qZKgS85CF2LCd39_nuYn_H2HFqnM9iayOhCx2pAhzaHBRR7hAKq1RmxlAe8mKUDa_Uh0k6CQm3ZdhWucHEBqir2lGO_IR2YmmMVWT25vprRFWj6O9qKKGxw_YQgjUGX3unZ6Px5S3tbtawZuJzWZSgbm62vqcpRf3JSVZIIVO1tSg13P0tQt_9QrHx9-kfWN0sQIOH7EHwHHl_Lep9dgfmB-z-RUu7ujxg-8FSl_xloJN-9YiZPh_V32DG300RItBHjujYB_8I6GHCrx8_z6lOGqeaaDNOWVmOA_L3zeFJXnven80A-JrkmE_nfLyAigJ1Pm5Lfz1mV4OzT2-HUSisEDmVx6sIRSDxMYuCsjorVOE1-NhUMgXpK18ZECKvrLAJxjegwFuv6BBs5TMNsSvkE7Y7r-dwyLiwLqdfsU7kUiUe3U0QXgoBJjbKx7LDXm--bOkC6zgVv5iVTfSRpiXJoQxy6LDnbe_rNdvGX_qdkpDaPsSR3dyoF5_LYHKlwkhIg0m9srkCawonEyN1pYR26KVXHfaCRFySJeOUnAkHEvDFiBOr7CPYoXuJLk2Hdbd6ogW6rebjoCT_mXR3o0FlAIpleavWR_9ufsru0WDr7E-X7a4WN_AM_aGV7bEdPTjvBdXvNVkFvF4OJ78BMLQIEQ
linkProvider ProQuest
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3NbhMxELaqIgQcEC0gUgL40AoQWnW99v4dEAqUNKFJ1EMr9WZs75hGirIlCVTceAfeg4fiSZjZ7KaKEHDqddfa9e7MfJ4Ze75hbDc2ziehtYHI8ixQOTi0OciD1CEUFrFMjKE85HCU9E7Vh7P4bIP9bGph6Fhlg4kVUBeloxz5Pp3EyjBWkcmbi88BdY2i3dWmhcZSLY7g2yWGbPPX_QOU714Udd-fvOsFdVeBwKk0XAT4fuk9WJylzZJc5T4DH5pCxiB94QsDQqSFFTZC5x4UeOsVVYAWPskgdES-hJB_Q0mZk0Vl3cMrkt-k4ujEWSZBhJbQHLSPY8oxRPtJLoWM1doSWHUKWK0HN88pEr8c_7EyVMtd9x67W_upvLNUrC22AdNtdme4Inmdb7OtGhfm_EVNXv3yPjMdPiq_woQfjBGQ0CMPqMiEDwD9Wfj1_cchdWXj1IFtwikHzPGBvF-VavLS885kAsCXlMp8POXHMygoLcCPV43GHrDTa_nhD9nmtJzCI8aFdSlt_DqRShV5dG5BeCkEmNAoH8oWe9X8We1qjnNqtTHRVawTx5rkoGs5tNjeavTFktvjL-PekpBWY4iRu7pQzj7p2sC1wrgrAxN7ZVMF1uRORkZmhRKZw5igaLHnJGJNuIFTcqYuf8APIwYu3UFoRWcWHagWa6-NRHt3a7d3ayX5z6TbjQbpGpbm-sqIdv59-xm71TsZDvSgPzp6zG7Tg5d5pzbbXMy-wBP0xBb2aaX-nH28bnv7DR0vQyc
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=A+Novel+Discrete-Time+Leslie-Gower+Model+with+the+Impact+of+Allee+Effect+in+Predator+Population&rft.jtitle=Complexity+%28New+York%2C+N.Y.%29&rft.au=Vinoth%2C+S&rft.au=Sivasamy%2C+R&rft.au=Sathiyanathan%2C+K&rft.au=Unyong%2C+B&rft.date=2022&rft.pub=John+Wiley+%26+Sons%2C+Inc&rft.issn=1076-2787&rft.volume=2022&rft_id=info:doi/10.1155%2F2022%2F6931354&rft.externalDocID=A832456381
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1076-2787&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1076-2787&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1076-2787&client=summon