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Volumn 37, Issue 5, 2008, Pages 1343-1355

Limit cycles in a generalized Gause-type predator-prey model

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; ECOSYSTEMS; FUNCTIONAL ANALYSIS; NUMERICAL METHODS;

EID: 40949093548     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2006.10.017     Document Type: Article
Times cited : (28)

References (38)
  • 1
    • 0034503328 scopus 로고    scopus 로고
    • The evolution of predator-prey interactions: theory and evidence
    • Abrams P.A. The evolution of predator-prey interactions: theory and evidence. Annu Rev Ecol Syst 31 (2000) 79-105
    • (2000) Annu Rev Ecol Syst , vol.31 , pp. 79-105
    • Abrams, P.A.1
  • 2
    • 0020363569 scopus 로고
    • Functional responses of optimal foragers
    • Abrams P.A. Functional responses of optimal foragers. Am. Nat. 120 (1982) 382-390
    • (1982) Am. Nat. , vol.120 , pp. 382-390
    • Abrams, P.A.1
  • 3
    • 0034255819 scopus 로고    scopus 로고
    • The nature of predation: prey dependent, ratio dependent or neither?
    • Abrams P.A., and Ginzburg L.R. The nature of predation: prey dependent, ratio dependent or neither?. TREE 15 (2000) 337-341
    • (2000) TREE , vol.15 , pp. 337-341
    • Abrams, P.A.1    Ginzburg, L.R.2
  • 4
    • 0007280433 scopus 로고
    • Stable limit cycles in prey-predator populations
    • Albrecht F., Gatzke H., and Wax N. Stable limit cycles in prey-predator populations. Science 181 (1973) 1073-1074
    • (1973) Science , vol.181 , pp. 1073-1074
    • Albrecht, F.1    Gatzke, H.2    Wax, N.3
  • 5
    • 1542648323 scopus 로고    scopus 로고
    • Predator-prey size-dependent functional response: derivation and rescaling to the real world
    • Aljetlawi A.A., Sparrevik E., and Leonardsson K. Predator-prey size-dependent functional response: derivation and rescaling to the real world. J Anim Ecol 73 (2004) 239-252
    • (2004) J Anim Ecol , vol.73 , pp. 239-252
    • Aljetlawi, A.A.1    Sparrevik, E.2    Leonardsson, K.3
  • 6
    • 0041868333 scopus 로고
    • Lyapunov functions for a generalized Gause-type model
    • Ardito A., and Ricciardi P. Lyapunov functions for a generalized Gause-type model. J Math Biol 33 (1995) 816-828
    • (1995) J Math Biol , vol.33 , pp. 816-828
    • Ardito, A.1    Ricciardi, P.2
  • 7
    • 0001747368 scopus 로고
    • Uniqueness of a limit cycle for predator-prey system
    • Cheng K.S. Uniqueness of a limit cycle for predator-prey system. SIAM J Math Anal 12 4 (1981) 541-548
    • (1981) SIAM J Math Anal , vol.12 , Issue.4 , pp. 541-548
    • Cheng, K.S.1
  • 9
    • 0002808656 scopus 로고
    • Global stability and persistence of simple food chains
    • Freedman H.I., and So J.W.-H. Global stability and persistence of simple food chains. Math Biosci 76 (1985) 69-86
    • (1985) Math Biosci , vol.76 , pp. 69-86
    • Freedman, H.I.1    So, J.W.-H.2
  • 10
    • 0002667239 scopus 로고
    • Further studies of interaction between predator and prey
    • Gause G.F., Smaragdova N.P., and Witt A.A. Further studies of interaction between predator and prey. J Anim Ecol 5 (1936) 1-18
    • (1936) J Anim Ecol , vol.5 , pp. 1-18
    • Gause, G.F.1    Smaragdova, N.P.2    Witt, A.A.3
  • 11
    • 0031957495 scopus 로고    scopus 로고
    • Assessing reproduction to be a function of consumption raises doubts about some popular predator-prey models
    • Ginzburg L.R. Assessing reproduction to be a function of consumption raises doubts about some popular predator-prey models. J Anim Ecol 67 (1998) 325-327
    • (1998) J Anim Ecol , vol.67 , pp. 325-327
    • Ginzburg, L.R.1
  • 12
    • 0034080981 scopus 로고    scopus 로고
    • Uniqueness of limit cycle in the predator-prey system with symmetric prey isocline
    • Hasík K. Uniqueness of limit cycle in the predator-prey system with symmetric prey isocline. Math Biosci 164 (2000) 203-215
    • (2000) Math Biosci , vol.164 , pp. 203-215
    • Hasík, K.1
  • 13
    • 0346695643 scopus 로고    scopus 로고
    • Nonexistence of limit cycles in a predator-prey system with a sigmoid functional response
    • Hesaaraki M., and Moghadas S.M. Nonexistence of limit cycles in a predator-prey system with a sigmoid functional response. Can Appl Math Quar 7 4 (1999) 401-408
    • (1999) Can Appl Math Quar , vol.7 , Issue.4 , pp. 401-408
    • Hesaaraki, M.1    Moghadas, S.M.2
  • 14
    • 0035420533 scopus 로고    scopus 로고
    • Existence of limit cycles for predator-prey systems with a class of functional responses
    • Hesaaraki M., and Moghadas S.M. Existence of limit cycles for predator-prey systems with a class of functional responses. Ecol Modell 142 (2001) 1-9
    • (2001) Ecol Modell , vol.142 , pp. 1-9
    • Hesaaraki, M.1    Moghadas, S.M.2
  • 15
    • 0025073957 scopus 로고
    • Multiple limit cycles for predator prey models
    • Hofbauer J., and So J.W.-H. Multiple limit cycles for predator prey models. Math Biosci 99 (1990) 71-75
    • (1990) Math Biosci , vol.99 , pp. 71-75
    • Hofbauer, J.1    So, J.W.-H.2
  • 16
    • 84888258034 scopus 로고
    • The components of predation as revealed by a study of small-mammal predation of the European pine sawfly
    • Holling C.S. The components of predation as revealed by a study of small-mammal predation of the European pine sawfly. Can Entomol 91 (1959) 293-320
    • (1959) Can Entomol , vol.91 , pp. 293-320
    • Holling, C.S.1
  • 17
    • 0002366911 scopus 로고
    • The functional response of predators to prey density and its role in mimicry and population regulation
    • Holling C.S. The functional response of predators to prey density and its role in mimicry and population regulation. Mem Entomol Soc Can 45 (1965) 1-60
    • (1965) Mem Entomol Soc Can , vol.45 , pp. 1-60
    • Holling, C.S.1
  • 19
    • 0036162215 scopus 로고    scopus 로고
    • Predator functional responses: discriminating between handling and digesting prey
    • Jeschke J.M., Kopp M., and Tollrian R. Predator functional responses: discriminating between handling and digesting prey. Ecol Monogr 72 1 (2002) 95-112
    • (2002) Ecol Monogr , vol.72 , Issue.1 , pp. 95-112
    • Jeschke, J.M.1    Kopp, M.2    Tollrian, R.3
  • 20
    • 2542425392 scopus 로고    scopus 로고
    • Consumer-food systems: why type I functional responses are exclusive to filter feeders
    • Jeschke J.M., Kopp M., and Tollrian R. Consumer-food systems: why type I functional responses are exclusive to filter feeders. Biol Rev 79 (2004) 337-349
    • (2004) Biol Rev , vol.79 , pp. 337-349
    • Jeschke, J.M.1    Kopp, M.2    Tollrian, R.3
  • 21
    • 0034702751 scopus 로고    scopus 로고
    • Testing for predator dependence in predator-prey dynamics: a non-parameteric approach
    • Jost C., and Ellner S.P. Testing for predator dependence in predator-prey dynamics: a non-parameteric approach. Proc R Soc Lond B 267 (2000) 1611-1620
    • (2000) Proc R Soc Lond B , vol.267 , pp. 1611-1620
    • Jost, C.1    Ellner, S.P.2
  • 22
    • 0030103140 scopus 로고    scopus 로고
    • A predator-prey model with Ivlev's functional response
    • Kooij R.E., and Zegeling A. A predator-prey model with Ivlev's functional response. J Math Anal Appl 188 (1996) 473-489
    • (1996) J Math Anal Appl , vol.188 , pp. 473-489
    • Kooij, R.E.1    Zegeling, A.2
  • 23
    • 0039645998 scopus 로고
    • Limit cycles in predator-prey communities
    • May R.M. Limit cycles in predator-prey communities. Science 177 (1972) 900-902
    • (1972) Science , vol.177 , pp. 900-902
    • May, R.M.1
  • 25
    • 0347956472 scopus 로고    scopus 로고
    • Some conditions for the nonexistence of limit cycles in a predator prey system
    • Moghadas S.M. Some conditions for the nonexistence of limit cycles in a predator prey system. Appl Anal 81 (2002) 51-67
    • (2002) Appl Anal , vol.81 , pp. 51-67
    • Moghadas, S.M.1
  • 26
    • 0347476983 scopus 로고    scopus 로고
    • A non-standard numerical scheme for a generalized Gause-type predator-prey model
    • Moghadas S.M., Alexander M.E., and Corbett B.D. A non-standard numerical scheme for a generalized Gause-type predator-prey model. Phys D 188 (2004) 134-151
    • (2004) Phys D , vol.188 , pp. 134-151
    • Moghadas, S.M.1    Alexander, M.E.2    Corbett, B.D.3
  • 27
    • 3142696453 scopus 로고    scopus 로고
    • Dynamics of a generalized Gause-type predator-prey model with a seasonal functional response
    • Moghadas S.M., and Alexander M.E. Dynamics of a generalized Gause-type predator-prey model with a seasonal functional response. Chaos, Solitons & Fractals 23 (2005) 55-65
    • (2005) Chaos, Solitons & Fractals , vol.23 , pp. 55-65
    • Moghadas, S.M.1    Alexander, M.E.2
  • 28
    • 0003475470 scopus 로고
    • Springer-Verlag, Berlin Heidelberg/New York
    • Murray J.D. Mathematical biology (1989), Springer-Verlag, Berlin Heidelberg/New York
    • (1989) Mathematical biology
    • Murray, J.D.1
  • 29
    • 0030499149 scopus 로고    scopus 로고
    • Stability, persistence and structural stability in a classical predator-prey model
    • Myerscough R.M., Darwen M.J., and Hogarth W.L. Stability, persistence and structural stability in a classical predator-prey model. Ecol Modelling 89 (1996) 31-42
    • (1996) Ecol Modelling , vol.89 , pp. 31-42
    • Myerscough, R.M.1    Darwen, M.J.2    Hogarth, W.L.3
  • 30
    • 0033842238 scopus 로고    scopus 로고
    • Numerical and functional responses of migrant bald Eagles exploiting a seasonally concentrated food source
    • Restani M., Harmata A.R., and Madden E.M. Numerical and functional responses of migrant bald Eagles exploiting a seasonally concentrated food source. The Condor 102 (2000) 561-568
    • (2000) The Condor , vol.102 , pp. 561-568
    • Restani, M.1    Harmata, A.R.2    Madden, E.M.3
  • 31
    • 0015243940 scopus 로고
    • Paradox of enrichment: destabilization of exploitation ecosystems in ecological time
    • Rosenzweig M.L. Paradox of enrichment: destabilization of exploitation ecosystems in ecological time. Science 171 (1971) 385-387
    • (1971) Science , vol.171 , pp. 385-387
    • Rosenzweig, M.L.1
  • 32
    • 0036099569 scopus 로고    scopus 로고
    • Functional response of a generalist insect predator to one of its prey species in the field
    • Schenk D., and Bacher S. Functional response of a generalist insect predator to one of its prey species in the field. J Anim Ecol 71 (2002) 524-531
    • (2002) J Anim Ecol , vol.71 , pp. 524-531
    • Schenk, D.1    Bacher, S.2
  • 33
    • 0001298237 scopus 로고
    • Optimal foraging: partial consumption of prey
    • Sih A. Optimal foraging: partial consumption of prey. Am Nat 116 2 (1980) 281-290
    • (1980) Am Nat , vol.116 , Issue.2 , pp. 281-290
    • Sih, A.1
  • 34
    • 0035658752 scopus 로고    scopus 로고
    • Functional responses with predator interference: viable alternatives to the Holling type II model
    • Skalski G.T., and Gilliam J.F. Functional responses with predator interference: viable alternatives to the Holling type II model. Ecology 82 11 (2001) 3083-3092
    • (2001) Ecology , vol.82 , Issue.11 , pp. 3083-3092
    • Skalski, G.T.1    Gilliam, J.F.2
  • 35
    • 0001628540 scopus 로고    scopus 로고
    • Two-parameter bifurcation in a predator-prey system of Ivlev type
    • Sugie J. Two-parameter bifurcation in a predator-prey system of Ivlev type. J Math Anal Appl 217 (1998) 349-371
    • (1998) J Math Anal Appl , vol.217 , pp. 349-371
    • Sugie, J.1
  • 36
    • 0000853045 scopus 로고
    • Nonexistence of periodic solutions of the Liénard system
    • Sugie J., and Hara T. Nonexistence of periodic solutions of the Liénard system. J Math Anal Appl 159 (1991) 224-236
    • (1991) J Math Anal Appl , vol.159 , pp. 224-236
    • Sugie, J.1    Hara, T.2
  • 37
    • 0007420124 scopus 로고    scopus 로고
    • On a predator-prey system of Holling type
    • Sugie J., Kohno R., and Miyazaki R. On a predator-prey system of Holling type. Proc Amer Math Soc 125 (1997) 2041-2050
    • (1997) Proc Amer Math Soc , vol.125 , pp. 2041-2050
    • Sugie, J.1    Kohno, R.2    Miyazaki, R.3
  • 38
    • 0025331493 scopus 로고
    • Limit cycles in predator-prey models
    • Wrzosek D.M. Limit cycles in predator-prey models. Math Biosci 98 (1990) 1-12
    • (1990) Math Biosci , vol.98 , pp. 1-12
    • Wrzosek, D.M.1


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