메뉴 건너뛰기




Volumn 14, Issue 4, 2013, Pages 1896-1906

Qualitative analysis of Holling type II predator-prey systems with prey refuges and predator restricts

Author keywords

Existence and uniqueness; Global stability; Limit cycle; Predator restrict; Predator prey system

Indexed keywords

EXISTENCE AND UNIQUENESS; GLOBAL STABILITY; LIMIT CYCLE; PREDATOR - PREY SYSTEM; PREDATOR RESTRICT;

EID: 84875265696     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2013.01.001     Document Type: Article
Times cited : (16)

References (26)
  • 2
    • 0001628540 scopus 로고    scopus 로고
    • Two-parameter bifurcation in a predator-prey system of Ivlev type
    • J. Sugie 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
  • 3
    • 0041868333 scopus 로고
    • Lyapunov functions for a generalized Gause-type model
    • A. Ardito, and P. Ricciardi 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
  • 5
    • 0002421472 scopus 로고    scopus 로고
    • Uniqueness of limit cycle for Gause-type predator-prey systems
    • T.W. Hwang Uniqueness of limit cycle for Gause-type predator-prey systems J. Math. Anal. Appl. 238 1999 179 195
    • (1999) J. Math. Anal. Appl. , vol.238 , pp. 179-195
    • Hwang, T.W.1
  • 6
    • 0035376255 scopus 로고    scopus 로고
    • Global analysis of the Michaelis-Menten type ratio-dependent predator-prey system
    • S.B. Hsu, T.W. Hwang, and Y. Kuang Global analysis of the Michaelis-Menten type ratio-dependent predator-prey system J. Math. Biol. 42 2001 489 506
    • (2001) J. Math. Biol. , vol.42 , pp. 489-506
    • Hsu, S.B.1    Hwang, T.W.2    Kuang, Y.3
  • 8
    • 0002861760 scopus 로고
    • Uniqueness of limit cycles in Gause-type predator-prey systems
    • Y. Kuang, and H.I. Freedman Uniqueness of limit cycles in Gause-type predator-prey systems Math. Biosci. 88 1988 67 84
    • (1988) Math. Biosci. , vol.88 , pp. 67-84
    • Kuang, Y.1    Freedman, H.I.2
  • 9
    • 0030103140 scopus 로고    scopus 로고
    • A predator-prey model with Ivlev's functional response
    • R.E. Kooij, and A. Zegeling A predator-prey model with Ivlev's functional response J. Math. Anal. Appl. 198 1996 473 489
    • (1996) J. Math. Anal. Appl. , vol.198 , pp. 473-489
    • Kooij, R.E.1    Zegeling, A.2
  • 10
    • 77954142280 scopus 로고    scopus 로고
    • Global dynamics of a predator-prey model
    • X.X. Liu, and Y.J. Lou Global dynamics of a predator-prey model J. Math. Anal. Appl. 371 2010 323 340
    • (2010) J. Math. Anal. Appl. , vol.371 , pp. 323-340
    • Liu, X.X.1    Lou, Y.J.2
  • 11
    • 33748902433 scopus 로고    scopus 로고
    • Dynamics in ratio-dependent predator-prey model with predator harvesting
    • D.M. Xiao, W.X. Li, and M.A. Han Dynamics in ratio-dependent predator-prey model with predator harvesting J. Math. Anal. Appl. 324 2006 14 29
    • (2006) J. Math. Anal. Appl. , vol.324 , pp. 14-29
    • Xiao, D.M.1    Li, W.X.2    Han, M.A.3
  • 12
    • 0242371742 scopus 로고    scopus 로고
    • On the uniqueness and nonexistence of limit cycles for predator-prey systems
    • D. Xiao, and Z. Zhang On the uniqueness and nonexistence of limit cycles for predator-prey systems Nonlinearity 16 2003 1185 1201
    • (2003) Nonlinearity , vol.16 , pp. 1185-1201
    • Xiao, D.1    Zhang, Z.2
  • 14
    • 0001030091 scopus 로고
    • Community structure, population control and competition
    • N.G. Hairston, F.E. Smith, and L.B. Slobodkin Community structure, population control and competition Am. Nat. 94 1960 412 425
    • (1960) Am. Nat. , vol.94 , pp. 412-425
    • Hairston, N.G.1    Smith, F.E.2    Slobodkin, L.B.3
  • 15
    • 0000793906 scopus 로고
    • A more functional response to predator-prey stability
    • S.A. Levin A more functional response to predator-prey stability Am. Nat. 110 1977 381 383
    • (1977) Am. Nat. , vol.110 , pp. 381-383
    • Levin, S.A.1
  • 16
    • 70350716708 scopus 로고    scopus 로고
    • Qualitative analysis of a predator-prey model with Holling type II functional response incorporating a constant prey refuge
    • L.J. Chen, F.D. Chen, and L.J. Chen Qualitative analysis of a predator-prey model with Holling type II functional response incorporating a constant prey refuge Nonlinear Anal-Real. 11 2010 246 252
    • (2010) Nonlinear Anal-Real. , vol.11 , pp. 246-252
    • Chen, L.J.1    Chen, F.D.2    Chen, L.J.3
  • 17
    • 0029105665 scopus 로고
    • Bifurcation and stability analysis of a temperature-dependent mite predator-prey interaction model incorporating a prey refuge
    • J.B. Collings Bifurcation and stability analysis of a temperature-dependent mite predator-prey interaction model incorporating a prey refuge Bull. Math. Biol. 57 1995 63 76
    • (1995) Bull. Math. Biol. , vol.57 , pp. 63-76
    • Collings, J.B.1
  • 18
    • 0348077455 scopus 로고    scopus 로고
    • Dynamic consequences of prey refuges in a simple model system: More prey, fewer predators and enhanced stability
    • E. González-Olivares, and R. Ramos-Jiliberto Dynamic consequences of prey refuges in a simple model system: more prey, fewer predators and enhanced stability Ecol. Model. 166 2003 135 146
    • (2003) Ecol. Model. , vol.166 , pp. 135-146
    • González-Olivares, E.1    Ramos-Jiliberto, R.2
  • 19
    • 0345487003 scopus 로고    scopus 로고
    • Effects of optimal antipredator behavior of prey on predator-prey dynamics: The role of refuges
    • V. Krivan Effects of optimal antipredator behavior of prey on predator-prey dynamics: the role of refuges Theor. Popul. Biol. 53 1998 131 142
    • (1998) Theor. Popul. Biol. , vol.53 , pp. 131-142
    • Krivan, V.1
  • 20
    • 0022666085 scopus 로고
    • The effects of refuges on predator-prey interactions: A reconsideration
    • J.N. McNair The effects of refuges on predator-prey interactions: a reconsideration Theor. Popul. Biol. 29 1986 38 63
    • (1986) Theor. Popul. Biol. , vol.29 , pp. 38-63
    • McNair, J.N.1
  • 21
    • 0002366911 scopus 로고
    • The functional response of predators to prey density and its role in mimicry and population regulations
    • C.S. Holling The functional response of predators to prey density and its role in mimicry and population regulations Mem. Entomol. Soc. Can. 45 1965 3 60
    • (1965) Mem. Entomol. Soc. Can. , vol.45 , pp. 3-60
    • Holling, C.S.1
  • 22
    • 0004382872 scopus 로고
    • Some criteria for the absence of limit cycles and for the existence of a single limit cycle
    • (in Russian). 891-897 (English translation)
    • L.A. Cherkas, and L.I. Zhilevich Some criteria for the absence of limit cycles and for the existence of a single limit cycle Differ. Uravn. 6 1970 1170 1178 (in Russian). 891-897 (English translation)
    • (1970) Differ. Uravn. , vol.6 , pp. 1170-1178
    • Cherkas, L.A.1    Zhilevich, L.I.2
  • 24
    • 34250124159 scopus 로고
    • The qualitative analysis of two species predator-prey model with Holling's type III functional response
    • J.P. Chen, and H.D. Zhang The qualitative analysis of two species predator-prey model with Holling's type III functional response Appl. Math. Mech. (English Ed.) 7 1986 77 86
    • (1986) Appl. Math. Mech. (English Ed.) , vol.7 , pp. 77-86
    • Chen, J.P.1    Zhang, H.D.2
  • 25
    • 33845878254 scopus 로고    scopus 로고
    • On the predator-prey system with Holling- (n + 1) functional response
    • W. Wang, and J.H. Sun On the predator-prey system with Holling- (n + 1) functional response Acta Math. Sin. 23 2007 1 6
    • (2007) Acta Math. Sin. , vol.23 , pp. 1-6
    • Wang, W.1    Sun, J.H.2
  • 26
    • 0031232497 scopus 로고    scopus 로고
    • Qualitative properties of two-dimensional predator-prey systems
    • R.E. Kooij, and A. Zegeling Qualitative properties of two-dimensional predator-prey systems Nonlinear Anal-Theor. 29 1997 693 715
    • (1997) Nonlinear Anal-Theor. , vol.29 , pp. 693-715
    • Kooij, R.E.1    Zegeling, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.