메뉴 건너뛰기




Volumn 42, Issue 1-2, 2005, Pages 31-44

Qualitative analysis of predator-prey models with Beddington-DeAngelis functional response and diffusion

Author keywords

Beddington DeAngelis predator prey model; Positive steady states; Qualitative analysis; Stability

Indexed keywords

COMPUTATION THEORY; COMPUTER SCIENCE; DIFFUSION; MATHEMATICAL MODELS; SYSTEM STABILITY;

EID: 26844511430     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2005.05.013     Document Type: Article
Times cited : (98)

References (30)
  • 1
    • 0038750243 scopus 로고    scopus 로고
    • On the dynamics of predator-prey models with Beddington-De Angelis functional response
    • R.S. Cantrell, and C. Cosner On the dynamics of predator-prey models with Beddington-De Angelis functional response J. Math. Anal. Appl. 257 2001 206 222
    • (2001) J. Math. Anal. Appl. , vol.257 , pp. 206-222
    • Cantrell, R.S.1    Cosner, C.2
  • 2
    • 0037670816 scopus 로고    scopus 로고
    • Global analysis of the predator-prey system with Beddington-De Angelis functional response
    • T.-W. Hwang Global analysis of the predator-prey system with Beddington-De Angelis functional response J. Math. Anal. Appl. 281 2002 395 401
    • (2002) J. Math. Anal. Appl. , vol.281 , pp. 395-401
    • Hwang, T.-W.1
  • 3
    • 0000076167 scopus 로고
    • Mutual interference between parasites or predators and its effect on searching efficiency
    • J.R. Beddington Mutual interference between parasites or predators and its effect on searching efficiency J. Animal Ecol. 44 1975 331 340
    • (1975) J. Animal Ecol. , vol.44 , pp. 331-340
    • Beddington, J.R.1
  • 5
    • 0002011401 scopus 로고
    • The chemical basis of morphogenesis
    • A. Turing The chemical basis of morphogenesis Philos. Trans. Royal Soc. B 237 1952 37 72
    • (1952) Philos. Trans. Royal Soc. B , vol.237 , pp. 37-72
    • Turing, A.1
  • 6
    • 0035277877 scopus 로고    scopus 로고
    • The stability of spike solutions to the one-dimensional Gierer-Meinhardt model
    • D. Iron, M.J. Ward, and J.C. Wei The stability of spike solutions to the one-dimensional Gierer-Meinhardt model Phys. D 150 1-2 2001 25 62
    • (2001) Phys. D , vol.150 , Issue.1-2 , pp. 25-62
    • Iron, D.1    Ward, M.J.2    Wei, J.C.3
  • 7
    • 0036067340 scopus 로고    scopus 로고
    • Asymmetric spike patterns for the one-dimensional Gierer-Meinhardt model: Equilibria and stability
    • M.J. Ward, and J.C. Wei Asymmetric spike patterns for the one-dimensional Gierer-Meinhardt model: Equilibria and stability Euro. J. Appl. Math. 13 3 2002 283 320
    • (2002) Euro. J. Appl. Math. , vol.13 , Issue.3 , pp. 283-320
    • Ward, M.J.1    Wei, J.C.2
  • 8
    • 0037137989 scopus 로고    scopus 로고
    • Spikes for the Gierer-Meinhardt system in two dimensions: The strong coupling case
    • J.C. Wei, and M. Winter Spikes for the Gierer-Meinhardt system in two dimensions: The strong coupling case J. Differential Equations 178 2 2002 478 518
    • (2002) J. Differential Equations , vol.178 , Issue.2 , pp. 478-518
    • Wei, J.C.1    Winter, M.2
  • 9
    • 0037050701 scopus 로고    scopus 로고
    • Mini-maximizer for reaction-diffusion systems with skew-gradient structure
    • E. Yanagida Mini-maximizer for reaction-diffusion systems with skew-gradient structure J. Differential Equations 179 1 2002 311 335
    • (2002) J. Differential Equations , vol.179 , Issue.1 , pp. 311-335
    • Yanagida, E.1
  • 10
    • 23044517800 scopus 로고    scopus 로고
    • A priori bounds and global existence of solutions of the steady-state Sel'kov model
    • F.A. Davidson, and B.P. Rynne A priori bounds and global existence of solutions of the steady-state Sel'kov model Proc. Roy. Soc. Edinburgh A 130 2000 507 516
    • (2000) Proc. Roy. Soc. Edinburgh a , vol.130 , pp. 507-516
    • Davidson, F.A.1    Rynne, B.P.2
  • 11
    • 0037845132 scopus 로고    scopus 로고
    • Nonconstant positive steady states of the Sel'kov model
    • M.X. Wang Nonconstant positive steady states of the Sel'kov model J. Differential Equations 190 2 2003 600 620
    • (2003) J. Differential Equations , vol.190 , Issue.2 , pp. 600-620
    • Wang, M.X.1
  • 12
    • 0038778726 scopus 로고
    • Global bifurcation in the Brusselator system
    • K.J. Brown, and F.A. Davidson Global bifurcation in the Brusselator system Nonlinear Anal. TMA 24 1995 1713 1725
    • (1995) Nonlinear Anal. TMA , vol.24 , pp. 1713-1725
    • Brown, K.J.1    Davidson, F.A.2
  • 13
    • 0002542873 scopus 로고    scopus 로고
    • Large amplitude stationary solutions to a chemotaxis systems
    • C.S. Lin, W.M. Ni, and I. Takagi Large amplitude stationary solutions to a chemotaxis systems J. Differential Equations 72 1998 1 27
    • (1998) J. Differential Equations , vol.72 , pp. 1-27
    • Lin, C.S.1    Ni, W.M.2    Takagi, I.3
  • 14
    • 0034376967 scopus 로고    scopus 로고
    • Qualitative behavior of solutions of chemotactic diffusion systems: Effects of motility and chemo-taxis and dynamics
    • X.F. Wang Qualitative behavior of solutions of chemotactic diffusion systems: Effects of motility and chemo-taxis and dynamics SIAM J. Math. Anal. 31 3 2000 535 560
    • (2000) SIAM J. Math. Anal. , vol.31 , Issue.3 , pp. 535-560
    • Wang, X.F.1
  • 15
    • 0347055376 scopus 로고    scopus 로고
    • On 3 × 3 Lotka-Volterra competition systems with cross-diffusion
    • Y. Lou, S. Martinez, and W.M. Ni On 3 × 3 Lotka-Volterra competition systems with cross-diffusion Discrete Contin. Dyn. Syst. 6 1 2000 175 190
    • (2000) Discrete Contin. Dyn. Syst. , vol.6 , Issue.1 , pp. 175-190
    • Lou, Y.1    Martinez, S.2    Ni, W.M.3
  • 16
    • 0030579038 scopus 로고    scopus 로고
    • Diffusion, self-diffusion and cross-diffusion
    • Y. Lou, and W.M. Ni Diffusion, self-diffusion and cross-diffusion J. Differential Equations 131 1996 79 131
    • (1996) J. Differential Equations , vol.131 , pp. 79-131
    • Lou, Y.1    Ni, W.M.2
  • 17
    • 0033130048 scopus 로고    scopus 로고
    • Diffusion vs. cross-diffusion: An elliptic approach
    • Y. Lou, and W.M. Ni Diffusion vs. cross-diffusion: An elliptic approach J. Differential Equations 154 1999 157 190
    • (1999) J. Differential Equations , vol.154 , pp. 157-190
    • Lou, Y.1    Ni, W.M.2
  • 18
    • 0003002827 scopus 로고    scopus 로고
    • Diffusion, cross-diffusion and their spike-layer steady states
    • W.M. Ni Diffusion, cross-diffusion and their spike-layer steady states Notices Amer. Math. Soc. 45 1 1998 9 18
    • (1998) Notices Amer. Math. Soc. , vol.45 , Issue.1 , pp. 9-18
    • Ni, W.M.1
  • 21
    • 23044527512 scopus 로고    scopus 로고
    • Qualitative behaviour of positive solutions of a predator-prey model: Effects of satura- tion
    • Y.H. Du, and Y. Lou Qualitative behaviour of positive solutions of a predator-prey model: Effects of satura- tion Proc. Roy. Soc. Edinburgh A 131 2001 321 349
    • (2001) Proc. Roy. Soc. Edinburgh a , vol.131 , pp. 321-349
    • Du, Y.H.1    Lou, Y.2
  • 22
    • 0002085758 scopus 로고
    • An interracial approach to regional segregation of two competing species mediated by a predator
    • T. Ikeda, and M. Mimura An interracial approach to regional segregation of two competing species mediated by a predator J. Math. Biol. 31 1993 215 240
    • (1993) J. Math. Biol. , vol.31 , pp. 215-240
    • Ikeda, T.1    Mimura, M.2
  • 23
    • 0034652878 scopus 로고    scopus 로고
    • Existence and instability of Neumann layer solutions for a 3-component Lotka-Volterra model with diffusion
    • Y. Kan-on Existence and instability of Neumann layer solutions for a 3-component Lotka-Volterra model with diffusion J. Math. Anal. Appl. 243 2000 357 372
    • (2000) J. Math. Anal. Appl. , vol.243 , pp. 357-372
    • Kan-On, Y.1
  • 24
    • 0032389543 scopus 로고    scopus 로고
    • Singular perturbation approach to a 3-component reaction-diffusion system arising in population dynamics
    • Y. Kan-on, and M. Mimura Singular perturbation approach to a 3-component reaction-diffusion system arising in population dynamics SIAM J. Math. Anal. 29 1998 1519 1536
    • (1998) SIAM J. Math. Anal. , vol.29 , pp. 1519-1536
    • Kan-On, Y.1    Mimura, M.2
  • 25
    • 1442279582 scopus 로고    scopus 로고
    • Nonconstant positive steady states of a predator-prey system with nonmonotonic functional response and diffusion
    • P.Y.H. Pang, and M.X. Wang Nonconstant positive steady states of a predator-prey system with nonmonotonic functional response and diffusion Proc. London Math. Soc. 88 2004 135 157
    • (2004) Proc. London Math. Soc. , vol.88 , pp. 135-157
    • Pang, P.Y.H.1    Wang, M.X.2
  • 26
    • 0141957171 scopus 로고    scopus 로고
    • Qualitative analysis of a ratio-dependent predator-prey system with diffusion
    • P.Y.H. Pang, and M.X. Wang Qualitative analysis of a ratio-dependent predator-prey system with diffusion Proc. Roy. Soc. Edinburgh A 133 4 2003 919 942
    • (2003) Proc. Roy. Soc. Edinburgh a , vol.133 , Issue.4 , pp. 919-942
    • Pang, P.Y.H.1    Wang, M.X.2
  • 27
    • 5544250703 scopus 로고
    • Experimental evidence of a sustained Turing-type equilibrium chemical pattern
    • V. Castets, E. Dulos, J. Boissonade, and P. DeKepper Experimental evidence of a sustained Turing-type equilibrium chemical pattern Phys. Rev. Lett. 64 1990 2953 2956
    • (1990) Phys. Rev. Lett. , vol.64 , pp. 2953-2956
    • Castets, V.1    Dulos, E.2    Boissonade, J.3    Dekepper, P.4
  • 28
    • 36449002257 scopus 로고
    • Dependence of Turing pattern wavelength on diffusion rate
    • Q. Ouyang, R. Li, G. Li, and H.L. Swinney Dependence of Turing pattern wavelength on diffusion rate Notices J. Chem. Phys. 102 1 1995 2551 2555
    • (1995) Notices J. Chem. Phys. , vol.102 , Issue.1 , pp. 2551-2555
    • Ouyang, Q.1    Li, R.2    Li, G.3    Swinney, H.L.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.