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Volumn 29, Issue 6, 1997, Pages 693-715

Qualitative properties of two-dimensional predator-prey systems

Author keywords

Li nard system; Limit cycle; Positive equilibrium

Indexed keywords

BIFURCATION (MATHEMATICS); DIFFERENTIATION (CALCULUS); ECOLOGY; FUNCTIONS; MATHEMATICAL TRANSFORMATIONS; PROBLEM SOLVING; THEOREM PROVING;

EID: 0031232497     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(96)00068-5     Document Type: Article
Times cited : (59)

References (27)
  • 1
    • 0002924819 scopus 로고
    • Variazioni e fluttuazioni del numero d'individui in specie animali conviventi
    • VOLTERRA V., Variazioni e fluttuazioni del numero d'individui in specie animali conviventi, Mem. R. Com. Tolassogr. Ital. 131, 1-142 (1927).
    • (1927) Mem. R. Com. Tolassogr. Ital. , vol.131 , pp. 1-142
    • Volterra, V.1
  • 4
    • 0000793906 scopus 로고
    • A more functional response to predator-prey stability
    • LEVIN S. A., A more functional response to predator-prey stability, Am. Nat. 110, 381-383 (1977).
    • (1977) Am. Nat. , vol.110 , pp. 381-383
    • Levin, S.A.1
  • 5
    • 0001524523 scopus 로고
    • Graphical representation and stability conditions of predator-prey interactions
    • ROSENZWEIG M. L. & MACARTHUR R. H., Graphical representation and stability conditions of predator-prey interactions, Am. Nat. 47, 209-223 (1963).
    • (1963) Am. Nat. , vol.47 , pp. 209-223
    • Rosenzweig, M.L.1    Macarthur, R.H.2
  • 6
    • 0001747368 scopus 로고
    • Uniqueness of a limit cycle for a predator-prey system
    • CHENG KUOSHENG, Uniqueness of a limit cycle for a predator-prey system, SIAM J. math. Analysis 12, 541-548 (1981).
    • (1981) SIAM J. Math. Analysis , vol.12 , pp. 541-548
    • Cheng, K.1
  • 7
    • 0002861760 scopus 로고
    • Uniqueness of limit cycles in Gause type models of predator prey systems
    • KUANG YANG & FREEDMAN H. I., Uniqueness of limit cycles in Gause type models of predator prey systems, Math. Biosci. 88, 67-84 (1988).
    • (1988) Math. Biosci. , vol.88 , pp. 67-84
    • Kuang, Y.1    Freedman, H.I.2
  • 8
    • 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, 293-320 (1959).
    • (1959) Can. Entomol. , vol.91 , pp. 293-320
    • Holling, C.S.1
  • 9
    • 34250124159 scopus 로고
    • The qualitative analysis of two species predator-prey model with Holling's type III functional response
    • CHEN JUNPING & ZHANG HONGDE, The qualitative analysis of two species predator-prey model with Holling's type III functional response, Appl. Math. Mech. 7, 77-86 (1986).
    • (1986) Appl. Math. Mech. , vol.7 , pp. 77-86
    • Chen, J.1    Zhang, H.2
  • 10
    • 0018098741 scopus 로고
    • A model predator-prey system with functional response
    • KAZANIROFF N. & VAN DER DRIESSCHE P., A model predator-prey system with functional response, Math. Biosci. 39, 125-134 (1978).
    • (1978) Math. Biosci. , vol.39 , pp. 125-134
    • Kazaniroff, N.1    Van Der Driessche, P.2
  • 11
    • 0025331493 scopus 로고
    • Limit cycles in predator-prey models
    • WRZOSEK D. M., Limit cycles in predator-prey models, Math. Biosci. 98, 1-12 (1990).
    • (1990) Math. Biosci. , vol.98 , pp. 1-12
    • Wrzosek, D.M.1
  • 12
    • 0022849138 scopus 로고
    • Predator-prey systems with group defense: The paradox of enrichment revisited
    • FREEDMAN H. I. & WOLKOWICZ G. S. K., Predator-prey systems with group defense: the paradox of enrichment revisited, Bull. math. Biol. 48, 493-508 (1986).
    • (1986) Bull. Math. Biol. , vol.48 , pp. 493-508
    • Freedman, H.I.1    Wolkowicz, G.S.K.2
  • 13
    • 0024448915 scopus 로고
    • Conditions for uniqueness of limit cycles in general predator-prey systems
    • HUANG XUNCHENG & MERRILL S. J., Conditions for uniqueness of limit cycles in general predator-prey systems, Math. Biosci. 96, 47-60 (1989).
    • (1989) Math. Biosci. , vol.96 , pp. 47-60
    • Huang, X.1    Merrill, S.J.2
  • 14
    • 0001084269 scopus 로고
    • On the uniqueness of limit cycles of certain equations of nonlinear oscillations
    • In Russian
    • ZHANG ZHIFEN, On the uniqueness of limit cycles of certain equations of nonlinear oscillations, Dokl. Acad. Nauk. SSSR 119, 659-662 (1958). (In Russian.)
    • (1958) Dokl. Acad. Nauk. SSSR , vol.119 , pp. 659-662
    • Zhang, Z.1
  • 15
    • 84953472772 scopus 로고
    • Proof of the uniqueness theorem of limit cycles of generalized Liénard equations
    • ZHANG ZHIFEN, Proof of the uniqueness theorem of limit cycles of generalized Liénard equations, Appl. Anal. 23, 63-76 (1986).
    • (1986) Appl. Anal. , vol.23 , pp. 63-76
    • Zhang, Z.1
  • 16
    • 0004382872 scopus 로고
    • Some criteria for the absence of limit cycles and for the existence of a single limit cycle
    • (Russian), 891-897 (English translation)
    • CHERKAS L. A. & ZHILEVICH L. I., Some criteria for the absence of limit cycles and for the existence of a single limit cycle, Diff. Urav. 6(7), 1170-1178 Russian), 891-897 (English translation) (1970).
    • (1970) Diff. Urav. , vol.6 , Issue.7 , pp. 1170-1178
    • Cherkas, L.A.1    Zhilevich, L.I.2
  • 17
    • 84974132694 scopus 로고
    • Quadratic systems with a degenerate critical point
    • COPPEL W. A., Quadratic systems with a degenerate critical point, Bull. Aust. math. Soc. 38, 1-10 (1988).
    • (1988) Bull. Aust. Math. Soc. , vol.38 , pp. 1-10
    • Coppel, W.A.1
  • 18
    • 0000883792 scopus 로고
    • A new class of quadratic systems
    • COPPEL W. A., A new class of quadratic systems, J. diff. Eqns 92(2), 360-372 (1991).
    • (1991) J. Diff. Eqns , vol.92 , Issue.2 , pp. 360-372
    • Coppel, W.A.1
  • 19
    • 84971760194 scopus 로고
    • On the uniqueness of limit cycles of the system dx/dt = φ(y) - F(x), dy/dt = -g(x)
    • In Chinese
    • WANG XIAN, On the uniqueness of limit cycles of the system dx/dt = φ(y) - F(x), dy/dt = -g(x), J. Nanjing Univ. 26(3), 363-372 (1990). (In Chinese.)
    • (1990) J. Nanjing Univ. , vol.26 , Issue.3 , pp. 363-372
    • Wang, X.1
  • 20
    • 84971708912 scopus 로고
    • Uniqueness of limit cycles in polynomial systems with algebraic invariants
    • ZEGELING A. & KOOIJ R. E., Uniqueness of limit cycles in polynomial systems with algebraic invariants, Bull. Aust. math. Soc. 49, 7-20 (1994).
    • (1994) Bull. Aust. Math. Soc. , vol.49 , pp. 7-20
    • Zegeling, A.1    Kooij, R.E.2
  • 21
    • 84972834610 scopus 로고
    • Nonuniqueness of limit cycles of Gause-type predator-prey systems
    • KUANG YANG, Nonuniqueness of limit cycles of Gause-type predator-prey systems, Appl. Analysis 29, 269-287 (1988).
    • (1988) Appl. Analysis , vol.29 , pp. 269-287
    • Kuang, Y.1
  • 22
    • 0042938573 scopus 로고
    • Transformations and their applications in planar quadratic systems
    • In Chinese
    • LIU JUN, Transformations and their applications in planar quadratic systems, J. Wuhan Iron and Steel College 4, 10-15 (1979). (In Chinese.)
    • (1979) J. Wuhan Iron and Steel College , vol.4 , pp. 10-15
    • Liu, J.1
  • 24
    • 0001469648 scopus 로고
    • Degenerate Hopf bifurcation in two dimension
    • KERTESZ V. & KOOIJ R. E., Degenerate Hopf bifurcation in two dimension, Nonlinear Analysis 17(3), 267-283 (1991).
    • (1991) Nonlinear Analysis , vol.17 , Issue.3 , pp. 267-283
    • Kertesz, V.1    Kooij, R.E.2
  • 25
    • 38249025380 scopus 로고
    • On the location and period of limit cycles in Gause-type predator-prey systems
    • KUANG YANG, On the location and period of limit cycles in Gause-type predator-prey systems, J. math. Analysis Applic. 142, 130-143 (1989).
    • (1989) J. Math. Analysis Applic. , vol.142 , pp. 130-143
    • Kuang, Y.1
  • 26
    • 0003804997 scopus 로고
    • Stability and Hopf bifurcation in a predator-prey system with several parameters
    • HAINZL J., Stability and Hopf bifurcation in a predator-prey system with several parameters, SIAM J. appl. Math. 48, 170-190 (1988).
    • (1988) SIAM J. Appl. Math. , vol.48 , pp. 170-190
    • Hainzl, J.1
  • 27
    • 0025068433 scopus 로고
    • On Liénard's equation and the uniqueness of limit cycles in predator-prey systems
    • MOREIRA H. N., On Liénard's equation and the uniqueness of limit cycles in predator-prey systems, J. Math. Biol. 28, 341-354 (1990).
    • (1990) J. Math. Biol. , vol.28 , pp. 341-354
    • Moreira, H.N.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.