On the Lotka–Volterra competition system with Allee effects

We study asymptotic dynamics of the classical Lotka–Volterra competition model when both competing populations are subject to Allee effects. The resulting system can have up to four interior steady states. In such case, it is proved that both competing populations may either go extinct, coexist, or...

Full description

Saved in:

Bibliographic Details
Published in	Computational and Applied Mathematics Vol. 32; no. 1; pp. 179 - 189
Main Author	Jang, Sophia R.-J.
Format	Journal Article
Language	English
Published	Basel SP Birkhäuser Verlag Basel 01.04.2013
Subjects	Applications of Mathematics Computational Mathematics and Numerical Analysis Mathematical Applications in Computer Science Mathematical Applications in the Physical Sciences Mathematics Mathematics and Statistics Allee effects Global stable manifolds 92D25 92D40 Monotone dynamical systems
Online Access	Get full text

Cover

Loading…

Abstract	We study asymptotic dynamics of the classical Lotka–Volterra competition model when both competing populations are subject to Allee effects. The resulting system can have up to four interior steady states. In such case, it is proved that both competing populations may either go extinct, coexist, or one population drives the other population to extinction depending on initial conditions.
AbstractList	We study asymptotic dynamics of the classical Lotka–Volterra competition model when both competing populations are subject to Allee effects. The resulting system can have up to four interior steady states. In such case, it is proved that both competing populations may either go extinct, coexist, or one population drives the other population to extinction depending on initial conditions.
Author	Jang, Sophia R.-J.
Author_xml	– sequence: 1 givenname: Sophia R.-J. surname: Jang fullname: Jang, Sophia R.-J. email: srjjang@gmail.com organization: Department of Mathematics and Statistics, Texas Tech University
BookMark	eNp9kD1OAzEQRi0UJELIAeh8AcOM7ay9BUUU8SdFogFay3JssmGzjmwjko47cENOwkahosg008wbfd87J4Mudp6QS4QrBFDXWYJAyQAFA-CcbU_IEDUoBgL4gAwBAZnmMDkj45xX0I8EQF4Nyc1TR8vS03ks7_bn6_s1tsWnZKmL640vTWliR_MuF7-mn01Z0mnbek99CN6VfEFOg22zH__tEXm5u32ePbD50_3jbDpnjmtdmNZ17WoMYhG0C1XldO1UgImtEZGrSgnprA9OSlEJjkIvYCJDrVS9QOACxIiow1-XYs7JB-OaYvfZSrJNaxDMXoQ5iDC9CLMXYbY9if_ITWrWNu2OMvzA5P62e_PJrOJH6vqCR6BfG0ByMQ
CitedBy_id	crossref_primary_10_1016_j_chaos_2023_113995 crossref_primary_10_1080_23737867_2017_1282843 crossref_primary_10_1186_s13662_018_1860_z crossref_primary_10_1142_S1793524523500778 crossref_primary_10_1016_j_matcom_2019_01_006
Cites_doi	10.1016/j.mbs.2003.06.001 10.1080/17513750903026429 10.1016/j.mbs.2007.02.006 10.1086/282171 10.1080/17513750802376313 10.1098/rspb.2004.2733 10.1080/10236190412331335373 10.1007/978-1-4612-0601-9 10.1016/j.tpb.2004.06.007 10.1080/00036811.2012.692365 10.5962/bhl.title.7226 10.1002/9781444313765 10.1016/S0304-3800(99)00160-X 10.1017/CBO9780511530043 10.2307/1937362 10.1093/acprof:oso/9780198570301.001.0001 10.1111/j.1939-7445.1989.tb00119.x 10.1137/1030003 10.1007/978-3-642-56166-5 10.1080/10236190500539238
ContentType	Journal Article
Copyright	SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2013
Copyright_xml	– notice: SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2013
DBID	AAYXX CITATION
DOI	10.1007/s40314-013-0022-x
DatabaseName	CrossRef
DatabaseTitle	CrossRef
DatabaseTitleList
DeliveryMethod	fulltext_linktorsrc
Discipline	Applied Sciences Mathematics
EISSN	1807-0302
EndPage	189
ExternalDocumentID	10_1007_s40314_013_0022_x
GroupedDBID	-EM .4S .DC 06D 0R~ 203 29F 2WC 30V 4.4 406 5GY 69Q 96X AAAVM AACDK AAHNG AAIAL AAJBT AAJKR AAKPC AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAZMS ABAKF ABDZT ABECU ABFTV ABJNI ABJOX ABKCH ABMQK ABQBU ABTEG ABTHY ABTKH ABTMW ABXHO ABXPI ACAOD ACCUX ACDTI ACGFO ACGFS ACHSB ACIPV ACIWK ACKNC ACMLO ACOKC ACPIV ACREN ACZOJ ADBBV ADHHG ADHIR ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADYOE ADZKW AEBTG AEFQL AEGNC AEGXH AEJHL AEJRE AEMSY AENEX AEOHA AEPYU AESKC AETCA AEVLU AEXYK AFBBN AFLOW AFQWF AFWTZ AFYQB AFZKB AGAYW AGDGC AGMZJ AGQEE AGQMX AGRTI AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AIAGR AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ AKLTO ALFXC ALMA_UNASSIGNED_HOLDINGS AMKLP AMTXH AMXSW AMYLF AMYQR ANMIH APOWU ARCSS ASPBG AUKKA AVWKF AXYYD AYJHY AZFZN BAPOH BGNMA C1A CS3 CSCUP DNIVK DPUIP DU5 E3Z EBLON EBS EDO EIOEI EJD ESBYG FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FYJPI GGCAI GGRSB GJIRD GQ7 HMJXF HRMNR HZ~ I0C IKXTQ IWAJR IXD J-C JBSCW JZLTJ KOV KQ8 KWQ LLZTM M4Y M~E NPVJJ NQJWS NU0 O9- O93 O9G O9J OK1 P2P PT4 RLLFE RNS ROL RSC RSV SCD SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE TR2 TSG UG4 UOJIU UTJUX UZXMN VFIZW W48 XSB Z7R Z83 ZMTXR AAYXX ABBRH ABDBE ABFSG ACMFV ACSTC AEZWR AFDZB AFHIU AFOHR AHPBZ AHWEU AIXLP AMVHM ATHPR AYFIA CITATION OVT
ID	FETCH-LOGICAL-c288t-8899c91f3df8cf66c89c7f05a9111276734caefc443632138d054f9779d102303
IEDL.DBID	AGYKE
ISSN	0101-8205
IngestDate	Thu Apr 24 23:11:47 EDT 2025 Tue Jul 01 00:45:58 EDT 2025 Fri Feb 21 02:27:55 EST 2025
IsPeerReviewed	true
IsScholarly	true
Issue	1
Keywords	Allee effects Global stable manifolds 92D25 92D40 Monotone dynamical systems
Language	English
License	http://www.springer.com/tdm
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c288t-8899c91f3df8cf66c89c7f05a9111276734caefc443632138d054f9779d102303
PageCount	11
ParticipantIDs	crossref_citationtrail_10_1007_s40314_013_0022_x crossref_primary_10_1007_s40314_013_0022_x springer_journals_10_1007_s40314_013_0022_x
ProviderPackageCode	CITATION AAYXX
PublicationCentury	2000
PublicationDate	2013-04-01
PublicationDateYYYYMMDD	2013-04-01
PublicationDate_xml	– month: 04 year: 2013 text: 2013-04-01 day: 01
PublicationDecade	2010
PublicationPlace	Basel
PublicationPlace_xml	– name: Basel
PublicationTitle	Computational and Applied Mathematics
PublicationTitleAbbrev	Comp. Appl. Math
PublicationYear	2013
Publisher	SP Birkhäuser Verlag Basel
Publisher_xml	– name: SP Birkhäuser Verlag Basel
References	SommerUWormBCompetition and Coexistence2002New YorkSpringer10.1007/978-3-642-56166-5 ZhouSWangGAllee-like effects in metapopulation dynamicsMath Biosci200418910311320549581073.9203910.1016/j.mbs.2003.06.001 Cushing JM (1988) The Allee effect in age-structured population dynamics. In: Hallam T, Gross L, Levin S (eds) Mathematical Ecology, pp 479–505 SmithHLWaltmanPThe Theory of Chemostat1995New YorkCambridge University Press0860.9203110.1017/CBO9780511530043 WalterWOrdinary Differential Equations, Graduate Texts in Mathematics1998New YorkSpringer10.1007/978-1-4612-0601-9 WangGLiangX-GWangF-ZThe competitive dynamics of populations subject to an Allee effectEcol Model199912418319210.1016/S0304-3800(99)00160-X HilkerFMPopulation collapse to extinction: the catastrophic combination of parasitism and Allee effectJ Biol Dyn2010486101260571110.1080/17513750903026429 HutchinsonGEThe paradox of the planktonAmer Natur19619513714510.1086/282171 VoornGHemerikLBoerMKooiBHeteroclinic orbits indicate overexploitation in predator-prey systems with a strong Allee effectMath Biosci200720945146923595591126.9206210.1016/j.mbs.2007.02.006 AllenLFaganJHognasGFagerhalmHPopulation extinction in discrete-time stochastic population models with an Allee effectJ Differ Equ Appl2005112732931064.9203610.1080/10236190412331335373 JangSR-JAllee effects in a discrete-time host-parasitoid modelJ Differ Equ Appl2006121651811088.9205810.1080/10236190500539238 Thieme HR (2005) Mathematics in Population Biology, Princeton University Press, Princeton SmithHLSystems of ordinary differential equations which generate an order preserving flow: a survey of resultsSIAM Rev198830871139312790674.3401210.1137/1030003 ZhouSLiuYWangGThe stability of predator-prey systems subject to the Allee effectsTheo Pop Biol20056723311072.9206010.1016/j.tpb.2004.06.007 Jang SR-J (2013) Competitive exclusion and coexistence in a Leslie-Gower competition model with Allee effects. Appl Anal doi:10.1080/00036811.2012.692365 ThiemeHRDhirasakdanonTHanZTrevinoRSpecies decline and extinction: synergy of infectious diseases and Allee effect?J Biol Dyn20093305323257401010.1080/17513750802376313 PringleCMNutrient spatial heterogeneity: effects on community structure, physiognomy, and diversity of stream algaeEcology19907190592010.2307/1937362 DennisBAllee effects, population growth, critical density, and the chance of extinctionNat Res Mod1989348153810371930850.92062 Begon M, Harper J, Townsend C (1996) Ecology: Individuals. Populations and Communities, Blackwell Science Ltd, New York MorozovAPetrovskiiSLiB-LBifurcations and chaos in a predator-prey system with the Allee effectProc Roy Soc Ser B20042711407141410.1098/rspb.2004.2733 Allee WC (1938) The Social Life of Animals, William Heinemann, University of Chicago Press, Chicago CourchampFBerecLGascoigneJAllee Effects in Ecology and Conservation2008New YorkOxford University Press10.1093/acprof:oso/9780198570301.001.0001 TilmanDResource Competition and Community Structure1982PrincetonPrinceton University Press D Tilman (22_CR18) 1982 F Courchamp (22_CR4) 2008 S Zhou (22_CR23) 2005; 67 B Dennis (22_CR6) 1989; 3 U Sommer (22_CR15) 2002 22_CR10 G Voorn (22_CR19) 2007; 209 A Morozov (22_CR11) 2004; 271 L Allen (22_CR2) 2005; 11 GE Hutchinson (22_CR7) 1961; 95 HL Smith (22_CR13) 1988; 30 CM Pringle (22_CR12) 1990; 71 SR-J Jang (22_CR9) 2006; 12 HL Smith (22_CR14) 1995 HR Thieme (22_CR17) 2009; 3 W Walter (22_CR20) 1998 FM Hilker (22_CR8) 2010; 4 22_CR16 S Zhou (22_CR22) 2004; 189 22_CR5 22_CR3 22_CR1 G Wang (22_CR21) 1999; 124
References_xml	– reference: PringleCMNutrient spatial heterogeneity: effects on community structure, physiognomy, and diversity of stream algaeEcology19907190592010.2307/1937362 – reference: HilkerFMPopulation collapse to extinction: the catastrophic combination of parasitism and Allee effectJ Biol Dyn2010486101260571110.1080/17513750903026429 – reference: TilmanDResource Competition and Community Structure1982PrincetonPrinceton University Press – reference: Begon M, Harper J, Townsend C (1996) Ecology: Individuals. Populations and Communities, Blackwell Science Ltd, New York – reference: VoornGHemerikLBoerMKooiBHeteroclinic orbits indicate overexploitation in predator-prey systems with a strong Allee effectMath Biosci200720945146923595591126.9206210.1016/j.mbs.2007.02.006 – reference: DennisBAllee effects, population growth, critical density, and the chance of extinctionNat Res Mod1989348153810371930850.92062 – reference: SommerUWormBCompetition and Coexistence2002New YorkSpringer10.1007/978-3-642-56166-5 – reference: WangGLiangX-GWangF-ZThe competitive dynamics of populations subject to an Allee effectEcol Model199912418319210.1016/S0304-3800(99)00160-X – reference: Thieme HR (2005) Mathematics in Population Biology, Princeton University Press, Princeton – reference: ZhouSWangGAllee-like effects in metapopulation dynamicsMath Biosci200418910311320549581073.9203910.1016/j.mbs.2003.06.001 – reference: Cushing JM (1988) The Allee effect in age-structured population dynamics. In: Hallam T, Gross L, Levin S (eds) Mathematical Ecology, pp 479–505 – reference: WalterWOrdinary Differential Equations, Graduate Texts in Mathematics1998New YorkSpringer10.1007/978-1-4612-0601-9 – reference: CourchampFBerecLGascoigneJAllee Effects in Ecology and Conservation2008New YorkOxford University Press10.1093/acprof:oso/9780198570301.001.0001 – reference: AllenLFaganJHognasGFagerhalmHPopulation extinction in discrete-time stochastic population models with an Allee effectJ Differ Equ Appl2005112732931064.9203610.1080/10236190412331335373 – reference: SmithHLWaltmanPThe Theory of Chemostat1995New YorkCambridge University Press0860.9203110.1017/CBO9780511530043 – reference: ThiemeHRDhirasakdanonTHanZTrevinoRSpecies decline and extinction: synergy of infectious diseases and Allee effect?J Biol Dyn20093305323257401010.1080/17513750802376313 – reference: Allee WC (1938) The Social Life of Animals, William Heinemann, University of Chicago Press, Chicago – reference: Jang SR-J (2013) Competitive exclusion and coexistence in a Leslie-Gower competition model with Allee effects. Appl Anal doi:10.1080/00036811.2012.692365 – reference: HutchinsonGEThe paradox of the planktonAmer Natur19619513714510.1086/282171 – reference: MorozovAPetrovskiiSLiB-LBifurcations and chaos in a predator-prey system with the Allee effectProc Roy Soc Ser B20042711407141410.1098/rspb.2004.2733 – reference: SmithHLSystems of ordinary differential equations which generate an order preserving flow: a survey of resultsSIAM Rev198830871139312790674.3401210.1137/1030003 – reference: JangSR-JAllee effects in a discrete-time host-parasitoid modelJ Differ Equ Appl2006121651811088.9205810.1080/10236190500539238 – reference: ZhouSLiuYWangGThe stability of predator-prey systems subject to the Allee effectsTheo Pop Biol20056723311072.9206010.1016/j.tpb.2004.06.007 – volume: 189 start-page: 103 year: 2004 ident: 22_CR22 publication-title: Math Biosci doi: 10.1016/j.mbs.2003.06.001 – volume: 4 start-page: 86 year: 2010 ident: 22_CR8 publication-title: J Biol Dyn doi: 10.1080/17513750903026429 – ident: 22_CR16 – volume: 209 start-page: 451 year: 2007 ident: 22_CR19 publication-title: Math Biosci doi: 10.1016/j.mbs.2007.02.006 – volume: 95 start-page: 137 year: 1961 ident: 22_CR7 publication-title: Amer Natur doi: 10.1086/282171 – volume: 3 start-page: 305 year: 2009 ident: 22_CR17 publication-title: J Biol Dyn doi: 10.1080/17513750802376313 – volume: 271 start-page: 1407 year: 2004 ident: 22_CR11 publication-title: Proc Roy Soc Ser B doi: 10.1098/rspb.2004.2733 – volume: 11 start-page: 273 year: 2005 ident: 22_CR2 publication-title: J Differ Equ Appl doi: 10.1080/10236190412331335373 – volume-title: Ordinary Differential Equations, Graduate Texts in Mathematics year: 1998 ident: 22_CR20 doi: 10.1007/978-1-4612-0601-9 – volume: 67 start-page: 23 year: 2005 ident: 22_CR23 publication-title: Theo Pop Biol doi: 10.1016/j.tpb.2004.06.007 – ident: 22_CR10 doi: 10.1080/00036811.2012.692365 – ident: 22_CR1 doi: 10.5962/bhl.title.7226 – ident: 22_CR3 doi: 10.1002/9781444313765 – volume: 124 start-page: 183 year: 1999 ident: 22_CR21 publication-title: Ecol Model doi: 10.1016/S0304-3800(99)00160-X – ident: 22_CR5 – volume-title: The Theory of Chemostat year: 1995 ident: 22_CR14 doi: 10.1017/CBO9780511530043 – volume: 71 start-page: 905 year: 1990 ident: 22_CR12 publication-title: Ecology doi: 10.2307/1937362 – volume-title: Allee Effects in Ecology and Conservation year: 2008 ident: 22_CR4 doi: 10.1093/acprof:oso/9780198570301.001.0001 – volume: 3 start-page: 481 year: 1989 ident: 22_CR6 publication-title: Nat Res Mod doi: 10.1111/j.1939-7445.1989.tb00119.x – volume: 30 start-page: 87 year: 1988 ident: 22_CR13 publication-title: SIAM Rev doi: 10.1137/1030003 – volume-title: Competition and Coexistence year: 2002 ident: 22_CR15 doi: 10.1007/978-3-642-56166-5 – volume: 12 start-page: 165 year: 2006 ident: 22_CR9 publication-title: J Differ Equ Appl doi: 10.1080/10236190500539238 – volume-title: Resource Competition and Community Structure year: 1982 ident: 22_CR18
SSID	ssj0000400126 ssj0037144
Score	1.9295912
Snippet	We study asymptotic dynamics of the classical Lotka–Volterra competition model when both competing populations are subject to Allee effects. The resulting...
SourceID	crossref springer
SourceType	Enrichment Source Index Database Publisher
StartPage	179
SubjectTerms	Applications of Mathematics Computational Mathematics and Numerical Analysis Mathematical Applications in Computer Science Mathematical Applications in the Physical Sciences Mathematics Mathematics and Statistics
Title	On the Lotka–Volterra competition system with Allee effects
URI	https://link.springer.com/article/10.1007/s40314-013-0022-x
Volume	32
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
link	http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV07T8MwED6hdoGBQgFRHpUHJlCq1HHzGBhaRKl4lKVFZYocN15apahJJcTEf-Af8ks4O05RESB1jHSxkrvz-bPv7jPAWRwHVKJhLUkZt5jnBpYvqeoC8QIeCMV4oqst-m5vyG5HrZHp406LavciJakj9bLZjSmmdUvfRqBK0BE4lhF-2KwE5fbN89330Yryy6ZCFXlAVpx0OcU37pxxwWsVyc3fBl1dnlZzo3rJ6VZgUHxsXmkyaSyyqCHefvA4rvk3O7BtIChp5z6zCxtxUoWKgaPETPa0ClsPS0rXdA8uHxOCj-R-lk345_vH00zl2eecCI28deUXyXmhiTrcJe3pNI6JqRfZh2H3enDVs8zdC5agvp9ZPu7DRNCUzlj6Qrqu8APhSbvFVXCknus5TPBYCsYc16FNxx8j9pMIJoOxIoOwnQMoJbMkPgQibBa5uKtDJIHw0La5QNDAKI042ibiogZ2ofJQGGJydT_GNFxSKmtlhaisUCkrfK3B-fKVl5yV4z_hi8IEoZmg6d_SR2tJH8Mm1TZUpjyBUjZfxKeIUrKojl7Z7XT6deOdXwQo2v4
linkProvider	Springer Nature
linkToHtml	http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV07T8MwELYQHYCBQgFRnh6YQKlSx81jYKgQpdAHS4vKFDmuvbRKUZNKiIn_wD_kl3B2nKAiQOoY6WIld2f7O9_dZ4QuhAiIBMNaklBmUc8NLF8S1QXiBSzgivFEV1v03faQPowaI9PHneTV7nlKUq_URbMbVUzrlr6NQJWgA3AsUQjBwa1LzbvnzvfRivLLukIV2YKsOOkyim-InGHDa-TJzd8GXd6elnOjestpldEg_9is0mRSW6RRjb_94HFc8W920LaBoLiZ-cwuWhNxBZUNHMVmsicVtNUrKF2TPXT9GGN4xN1ZOmGf7x9PM5VnnzPMNfLWlV8444XG6nAXN6dTIbCpF9lHw9bt4KZtmbsXLE58P7V8iMN4UJfOWPpcui73A-5Ju8HU4kg813MoZ0JySh3XIXXHHwP2kwAmg7Eig7CdA7Qez2JxiDC3aeRCVAdIAuChbTMOoIESEjGwTcR4Fdm5ykNuiMnV_RjTsKBU1soKQVmhUlb4WkWXxSsvGSvHf8JXuQlCM0GTv6WPVpI-RxvtQa8bdu_7nWO0SbQ9lVlP0Ho6X4hTQCxpdGY89AuTP9xx
linkToPdf	http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpZ3PT8IwFMdfDCRGD6KoEX_24EkzHF3Zj4MHoiIKogcxeJpd114gg7CRGE_-D_6H_iW2W4fBqInxuKRbtve69tu-188DOOTcw0I61hCYUIM4tme4AqtTII5HPaaIJ2m2Rddu9ch1v97XdU7jPNs9D0lmZxoUpSlKTsahOJkdfCOKum6klQlUOroUkUWi0HYFKDYuH9uf2yyqj9aUwsgGZ8Wny3DfchUtJ796Huj87qHzU9V8nDSdfpoleMpfPMs6GVSnSVBlL1-Yjv_4slVY0dIUNbK-tAYLPCpDSctUpAeBuAzLNzPUa7wOp7cRkpeoM0oG9P317WGk4u8TiliqyNOMMJTxopHa9EWN4ZBzpPNINqDXvLg_axm6JoPBsOsmhivXZ8yrCSsULhO2zVyPOcKsUzVoYsd2LMIoF4wQy7ZwzXJDqQmFFJleqCARprUJhWgU8S1AzCSBLVd7UmFI2WialEkxQTAOqPRTQFkFzNz8PtPAclU3Y-jPUMupsXxpLF8Zy3-uwNHslnFG6_it8XHuDl__uPHPrbf_1PoAFu_Om37nqtvegSWculN5dRcKyWTK96SQSYJ93Vk_ALIt5VU
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=On+the+Lotka%E2%80%93Volterra+competition+system+with+Allee+effects&rft.jtitle=Computational+and+Applied+Mathematics&rft.au=Jang%2C+Sophia+R.-J.&rft.date=2013-04-01&rft.issn=0101-8205&rft.eissn=1807-0302&rft.volume=32&rft.issue=1&rft.spage=179&rft.epage=189&rft_id=info:doi/10.1007%2Fs40314-013-0022-x&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s40314_013_0022_x
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0101-8205&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0101-8205&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0101-8205&client=summon