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Volumn 35, Issue 8, 2012, Pages 963-975

Limit cycles in a Gause-type predator-prey model with sigmoid functional response and weak Allee effect on prey

Author keywords

Allee effect; bifurcation; limit cycle; predator prey models; sigmoid functional response

Indexed keywords

ALLEE EFFECT; CAREFUL MANAGEMENT; FUNCTIONAL RESPONSE; GLOBAL BEHAVIORS; LIMIT CYCLE; LIMIT SETS; PARAMETER CONSTRAINTS; POSITIVE EQUILIBRIUM; PREDATOR-PREY MODELS; SADDLE POINT; STABLE LIMIT CYCLE;

EID: 84861348841     PISSN: 01704214     EISSN: 10991476     Source Type: Journal    
DOI: 10.1002/mma.2509     Document Type: Article
Times cited : (20)

References (42)
  • 3
    • 0033215101 scopus 로고    scopus 로고
    • Consequences of the Allee effect for behaviour, ecology and conservation
    • DOI 10.1016/S0169-5347(99)01684-5
    • Stephens PA, Sutherland WJ,. Consequences of the Allee effect for behaviour, ecology and conservation. Trends in Ecology and Evolution 1999; 14: 401-405. (Pubitemid 29428465)
    • (1999) Trends in Ecology and Evolution , vol.14 , Issue.10 , pp. 401-405
    • Stephens, P.A.1    Sutherland, W.J.2
  • 4
    • 0000073691 scopus 로고
    • Qualitative analysis of insect outbreak systems: The spruce budworm and forest
    • Ludwig D, Jones DD, Holling CS,. Qualitative analysis of insect outbreak systems: the spruce budworm and forest. Journal of Animal Ecology 1978; 36: 204-221.
    • (1978) Journal of Animal Ecology , vol.36 , pp. 204-221
    • Ludwig, D.1    Jones, D.D.2    Holling, C.S.3
  • 5
    • 0343364800 scopus 로고    scopus 로고
    • Absence of limit cycles of a predator-prey system with a sigmoid functional response
    • DOI 10.1016/0893-9659(96)00056-0
    • Sugie J, Miyamoto K, Morino K,. Absence of limits cycle of a predator-prey system with a sigmoid functional response. Applied Mathematical Letters 1996; 9: 85-90. (Pubitemid 126365308)
    • (1996) Applied Mathematics Letters , vol.9 , Issue.4 , pp. 85-90
    • Sugie, J.1    Miyamoto, K.2    Morino, K.3
  • 9
    • 84972834610 scopus 로고
    • Nonuniqueness of limit cycles of Gause-type predator-prey systems
    • Kuang Y,. Nonuniqueness of limit cycles of Gause-type predator-prey systems. Applicable Analysis 1988; 29: 269-287.
    • (1988) Applicable Analysis , vol.29 , pp. 269-287
    • Kuang, Y.1
  • 10
    • 79951508642 scopus 로고    scopus 로고
    • Predator-prey system with strong Allee effect in prey
    • Wang J, Shi J, Wei J,. Predator-prey system with strong Allee effect in prey. Journal of Mathematical Biology 2011; 62: 291-331.
    • (2011) Journal of Mathematical Biology , vol.62 , pp. 291-331
    • Wang, J.1    Shi, J.2    Wei, J.3
  • 11
    • 0242371742 scopus 로고    scopus 로고
    • On the uniqueness and nonexistence of limit cycles for predator-prey systems
    • Xiao D, Zhang Z,. On the uniqueness and nonexistence of limit cycles for predator-prey systems. Nonlinearity 2003; 16: 1185-1201.
    • (2003) Nonlinearity , vol.16 , pp. 1185-1201
    • Xiao, D.1    Zhang, Z.2
  • 12
    • 0002861760 scopus 로고
    • Uniqueness of limit cycles in Gause type models of predator-prey systems
    • Kuang Y, Freedman HI,. Uniqueness of limit cycles in Gause type models of predator-prey systems. Mathematical Biociences 1988; 88: 67-84.
    • (1988) Mathematical Biociences , vol.88 , pp. 67-84
    • Kuang, Y.1    Freedman, H.I.2
  • 13
    • 33845878254 scopus 로고    scopus 로고
    • On the predator-prey system with Holling-(n + 1) functional response
    • Wang W, Sun J-H,. On the predator-prey system with Holling-(n + 1) functional response. Acta Mathematica Sinica 2007; 23: 1-6.
    • (2007) Acta Mathematica Sinica , vol.23 , pp. 1-6
    • Wang, W.1    Sun, J.-H.2
  • 16
    • 0041175123 scopus 로고
    • Hilbert's 16th problem: How many cycles?
    • In, Braun M. Coleman C.S. Drew D. (eds). Springer Verlag.
    • Coleman CS,. Hilbert's 16th problem: how many cycles? In Differential Equations Model, Braun M, Coleman CS, Drew D, (eds). Springer Verlag, 1983; 279-297.
    • (1983) Differential Equations Model , pp. 279-297
    • Coleman, C.S.1
  • 17
    • 0030435677 scopus 로고    scopus 로고
    • A hypothesis regarding the abruptness of density dependence and the growth rate populations
    • Getz WM,. A hypothesis regarding the abruptness of density dependence and the growth rate populations. Ecology 1996; 77: 2014-2026.
    • (1996) Ecology , vol.77 , pp. 2014-2026
    • Getz, W.M.1
  • 18
    • 0038450626 scopus 로고    scopus 로고
    • Monographs in Population Biology, Princeton University Press: Princeton, NJ.
    • Murdoch WW, Briggs CJ, Nisbet RM,. Consumer-resources dynamics, Monographs in Population Biology, Vol. 36. Princeton University Press: Princeton, NJ, 2003.
    • (2003) Consumer-resources Dynamics , vol.36
    • Murdoch, W.W.1    Briggs, C.J.2    Nisbet, R.M.3
  • 20
    • 0000604313 scopus 로고
    • Allee effects: Population growth, critical density, and the chance of extinction
    • Dennis B,. Allee effects: population growth, critical density, and the chance of extinction. Natural Resource Modeling 1989; 3: 481-538.
    • (1989) Natural Resource Modeling , vol.3 , pp. 481-538
    • Dennis, B.1
  • 21
    • 33947307582 scopus 로고    scopus 로고
    • Multiple Allee effects and population management
    • DOI 10.1016/j.tree.2006.12.002, PII S0169534706003818
    • Berec L, Angulo E, Courchamp F,. Multiple Allee effects and population management. Trends in Ecology and Evolution 2007; 22: 185-191. (Pubitemid 46437275)
    • (2007) Trends in Ecology and Evolution , vol.22 , Issue.4 , pp. 185-191
    • Berec, L.1    Angulo, E.2    Courchamp, F.3
  • 24
    • 0022766987 scopus 로고
    • Global analysis of a system of predator-prey equations
    • Conway ED, Smoller JA,. Global analysis of a system of predator-prey equations. SIAM Journal on Applied Mathematics 1986; 46: 630-642. (Pubitemid 16607826)
    • (1986) SIAM Journal on Applied Mathematics , vol.46 , Issue.4 , pp. 630-642
    • Conway, E.D.1    Smoller, J.A.2
  • 27
    • 34548565990 scopus 로고    scopus 로고
    • Heteroclinic orbits indicate overexploitation in predator-prey systems with a strong Allee effect
    • DOI 10.1016/j.mbs.2007.02.006, PII S0025556407000363
    • van Voorn GAK, Hemerik L, Boer MP, Kooi BW,. Heteroclinic orbits indicate overexploitation in predator-prey systems with a strong Allee effect. Mathematical Biosciences 2007; 209: 451-469. (Pubitemid 47390913)
    • (2007) Mathematical Biosciences , vol.209 , Issue.2 , pp. 451-469
    • Van Voorn, G.A.K.1    Hemerik, L.2    Boer, M.P.3    Kooi, B.W.4
  • 28
    • 0035012881 scopus 로고    scopus 로고
    • Speeds of invasion in a model with strong or weak Allee effects
    • DOI 10.1016/S0025-5564(01)00048-7, PII S0025556401000487
    • Wang M-H, Kot M,. Speeds of invasion in a model with strong or weak Allee effects. Mathematical Biociences 2001; 171: 83-97. (Pubitemid 32429044)
    • (2001) Mathematical Biosciences , vol.171 , Issue.1 , pp. 83-97
    • Wang, M.-H.1    Kot, M.2
  • 31
    • 0035017349 scopus 로고    scopus 로고
    • Depensation: Evidence, models and implications
    • DOI 10.1046/j.1467-2979.2001.00029.x
    • Liermann M, Hilborn R,. Depensation: evidence, models and implications. Fish and Fisheries 2001; 2: 33-58. (Pubitemid 32437481)
    • (2001) Fish and Fisheries , vol.2 , Issue.1 , pp. 33-58
    • Liermann, M.1    Hilborn, R.2
  • 32
    • 0036399391 scopus 로고    scopus 로고
    • Single-species models of the Allee effect: Extinction boundaries, sex ratios and mate encounters
    • DOI 10.1006/jtbi.2002.3084
    • Boukal DS, Berec L,. Single-species models and the Allee effect: extinction boundaries, sex ratios and mate encounters. Journal of Theoretical Biology 2002; 218: 375-394. (Pubitemid 35191835)
    • (2002) Journal of Theoretical Biology , vol.218 , Issue.3 , pp. 375-394
    • Boukal, D.S.1    Berec, L.2
  • 36
    • 79955543665 scopus 로고    scopus 로고
    • Metastability in a Gause type predator-prey models with sigmoid functional response and multiplicative Allee effect on prey
    • In, Mondaini R. (ed.). E-papers Serviços Editoriais Ltda: Rio de Janeiro.
    • Rojas-Palma A, González-Olivares E, González-Yañez B,. Metastability in a Gause type predator-prey models with sigmoid functional response and multiplicative Allee effect on prey. In Proceedings of International Symposium on Mathematical and Computational Biology BIOMAT 2006, Mondaini R, (ed.). E-papers Serviços Editoriais Ltda: Rio de Janeiro, 2007; 295-321.
    • (2007) Proceedings of International Symposium on Mathematical and Computational Biology BIOMAT 2006 , pp. 295-321
    • Rojas-Palma, A.1    González-Olivares, E.2    González-Yañez, B.3
  • 38
    • 79955547730 scopus 로고    scopus 로고
    • Multiple limit cycles in a Gause type predator-prey model with Holling type III functional response and Allee effect on prey
    • González-Olivares E, Rojas-Palma A., Multiple limit cycles in a Gause type predator-prey model with Holling type III functional response and Allee effect on prey. Bulletin of Mathematical Biology 2011; 73: 1378-1397.
    • (2011) Bulletin of Mathematical Biology , vol.73 , pp. 1378-1397
    • González-Olivares, E.1    Rojas-Palma, A.2
  • 42
    • 51349134833 scopus 로고    scopus 로고
    • Consequences of Allee effect on a Gause type predator-prey model with nonmonotonic functional response
    • In, Mondaini R. (ed.). E-Papers Serviços Editoriais Ltda: Río de Janeiro.
    • González-Yañez B, González-Olivares E,. Consequences of Allee effect on a Gause type predator-prey model with nonmonotonic functional response. In Proceedings of the Third Brazilian Symposium on Mathematical and Computational Biology, Vol. 2, Mondaini R, (ed.). E-Papers Serviços Editoriais Ltda: Río de Janeiro, 2004; 358-373.
    • (2004) Proceedings of the Third Brazilian Symposium on Mathematical and Computational Biology , vol.2 , pp. 358-373
    • González-Yañez, B.1    González-Olivares, E.2


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