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Volumn 229, Issue 1, 2006, Pages 63-91

A diffusive predator-prey model with a protection zone

Author keywords

Predator prey model; Protection zone; Reaction diffusion system

Indexed keywords


EID: 33746733702     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2006.01.013     Document Type: Article
Times cited : (145)

References (43)
  • 1
    • 0001339498 scopus 로고
    • Global bifurcation of positive solutions in some systems of elliptic equations
    • Blat J., and Brown K.J. Global bifurcation of positive solutions in some systems of elliptic equations. SIAM J. Math. Anal. 17 (1986) 1339-1353
    • (1986) SIAM J. Math. Anal. , vol.17 , pp. 1339-1353
    • Blat, J.1    Brown, K.J.2
  • 2
  • 3
    • 2942630398 scopus 로고    scopus 로고
    • Spatial Ecology via Reaction-Diffusion Equation
    • John Wiley and Sons
    • Cantrell R.S., and Cosner C. Spatial Ecology via Reaction-Diffusion Equation. Wiley Ser. Math. Comput. Biol. (2003), John Wiley and Sons
    • (2003) Wiley Ser. Math. Comput. Biol.
    • Cantrell, R.S.1    Cosner, C.2
  • 4
    • 84972537529 scopus 로고
    • Existence and uniqueness of coexistence states for a predator-prey model with diffusion
    • Casal A., Eilbeck J.C., and López-Gómez J. Existence and uniqueness of coexistence states for a predator-prey model with diffusion. Differential Integral Equations 7 2 (1994) 411-439
    • (1994) Differential Integral Equations , vol.7 , Issue.2 , pp. 411-439
    • Casal, A.1    Eilbeck, J.C.2    López-Gómez, J.3
  • 5
    • 0021618680 scopus 로고
    • Stable coexistence state in the Volterra-Lotka competition model with diffusion
    • Cosner C., and Lazer A.C. Stable coexistence state in the Volterra-Lotka competition model with diffusion. SIAM J. Appl. Math. 44 (1984) 1112-1132
    • (1984) SIAM J. Appl. Math. , vol.44 , pp. 1112-1132
    • Cosner, C.1    Lazer, A.C.2
  • 7
    • 0000695246 scopus 로고
    • On positive solutions of some pairs of differential equations, II
    • Dancer E.N. On positive solutions of some pairs of differential equations, II. J. Differential Equations 60 (1985) 236-258
    • (1985) J. Differential Equations , vol.60 , pp. 236-258
    • Dancer, E.N.1
  • 8
    • 84966251421 scopus 로고
    • On the existence and uniqueness of positive solutions for competing species models with diffusion
    • Dancer E.N. On the existence and uniqueness of positive solutions for competing species models with diffusion. Trans. Amer. Math. Soc. 326 (1991) 829-859
    • (1991) Trans. Amer. Math. Soc. , vol.326 , pp. 829-859
    • Dancer, E.N.1
  • 9
    • 0001185909 scopus 로고
    • Competing species equations with diffusion, large interactions, and jumping nonlinearities
    • Dancer E.N., and Du Y. Competing species equations with diffusion, large interactions, and jumping nonlinearities. J. Differential Equations 114 (1994) 434-475
    • (1994) J. Differential Equations , vol.114 , pp. 434-475
    • Dancer, E.N.1    Du, Y.2
  • 10
    • 0037243354 scopus 로고    scopus 로고
    • Effects of certain degeneracies in the predator-prey model
    • Dancer E.N., and Du Y. Effects of certain degeneracies in the predator-prey model. SIAM J. Math. Anal. 34 2 (2002) 292-314
    • (2002) SIAM J. Math. Anal. , vol.34 , Issue.2 , pp. 292-314
    • Dancer, E.N.1    Du, Y.2
  • 11
    • 84972497506 scopus 로고
    • On the spectrum of some linear noncooperative elliptic systems with radial symmetry
    • Dancer E.N., López-Gómez J., and Ortega R. On the spectrum of some linear noncooperative elliptic systems with radial symmetry. Differential Integral Equations 8 3 (1995) 515-523
    • (1995) Differential Integral Equations , vol.8 , Issue.3 , pp. 515-523
    • Dancer, E.N.1    López-Gómez, J.2    Ortega, R.3
  • 12
    • 0018737036 scopus 로고
    • Convergence to homogeneous equilibrium state for generalized Volterra-Lotka systems
    • de Motoni P., and Rothe F. Convergence to homogeneous equilibrium state for generalized Volterra-Lotka systems. SIAM J. Appl. Math. 37 (1979) 648-663
    • (1979) SIAM J. Appl. Math. , vol.37 , pp. 648-663
    • de Motoni, P.1    Rothe, F.2
  • 13
    • 0036573310 scopus 로고    scopus 로고
    • Effects of a degeneracy in the competition model. I. Classical and generalized steady-state solutions
    • Du Y. Effects of a degeneracy in the competition model. I. Classical and generalized steady-state solutions. J. Differential Equations 181 1 (2002) 92-132
    • (2002) J. Differential Equations , vol.181 , Issue.1 , pp. 92-132
    • Du, Y.1
  • 14
    • 0036572632 scopus 로고    scopus 로고
    • Effects of a degeneracy in the competition model. II. Perturbation and dynamical behaviour
    • Du Y. Effects of a degeneracy in the competition model. II. Perturbation and dynamical behaviour. J. Differential Equations 181 1 (2002) 133-164
    • (2002) J. Differential Equations , vol.181 , Issue.1 , pp. 133-164
    • Du, Y.1
  • 15
    • 0041513380 scopus 로고    scopus 로고
    • Realization of prescribed patterns in the competition model
    • Du Y. Realization of prescribed patterns in the competition model. J. Differential Equations 193 1 (2003) 147-179
    • (2003) J. Differential Equations , vol.193 , Issue.1 , pp. 147-179
    • Du, Y.1
  • 16
    • 3342878930 scopus 로고    scopus 로고
    • Spatial patterns for population models in a heterogeneous environment
    • Du Y. Spatial patterns for population models in a heterogeneous environment. Taiwanese J. Math. 8 2 (2004) 155-182
    • (2004) Taiwanese J. Math. , vol.8 , Issue.2 , pp. 155-182
    • Du, Y.1
  • 17
    • 33746682335 scopus 로고    scopus 로고
    • Bifurcation and related topics in elliptic problems
    • Chipot M., and Quittner P. (Eds), Elsevier
    • Du Y. Bifurcation and related topics in elliptic problems. In: Chipot M., and Quittner P. (Eds). Handbook of Partial Differential Equations vol. 2 (2005), Elsevier 127-209
    • (2005) Handbook of Partial Differential Equations , vol.2 , pp. 127-209
    • Du, Y.1
  • 18
    • 33644516937 scopus 로고    scopus 로고
    • The degenerate logistic model and a singularly mixed boundary blow-up problem
    • Du Y., and Guo Z. The degenerate logistic model and a singularly mixed boundary blow-up problem. Discrete Contin. Dyn. Syst. 14 1 (2006) 1-29
    • (2006) Discrete Contin. Dyn. Syst. , vol.14 , Issue.1 , pp. 1-29
    • Du, Y.1    Guo, Z.2
  • 19
    • 3343010401 scopus 로고    scopus 로고
    • A diffusive predator-prey model in heterogeneous environment
    • Du Y., and Hsu S.-B. A diffusive predator-prey model in heterogeneous environment. J. Differential Equations 203 2 (2004) 331-364
    • (2004) J. Differential Equations , vol.203 , Issue.2 , pp. 331-364
    • Du, Y.1    Hsu, S.-B.2
  • 20
    • 21744459836 scopus 로고    scopus 로고
    • Some uniqueness and exact multiplicity results for a predator-prey model
    • Du Y., and Lou Y. Some uniqueness and exact multiplicity results for a predator-prey model. Trans. Amer. Math. Soc. 349 6 (1997) 2443-2475
    • (1997) Trans. Amer. Math. Soc. , vol.349 , Issue.6 , pp. 2443-2475
    • Du, Y.1    Lou, Y.2
  • 21
    • 0001674774 scopus 로고    scopus 로고
    • S-shaped global bifurcation curve and Hopf bifurcation of positive solutions to a predator-prey model
    • Du Y., and Lou Y. S-shaped global bifurcation curve and Hopf bifurcation of positive solutions to a predator-prey model. J. Differential Equations 144 2 (1998) 390-440
    • (1998) J. Differential Equations , vol.144 , Issue.2 , pp. 390-440
    • Du, Y.1    Lou, Y.2
  • 22
    • 23044527512 scopus 로고    scopus 로고
    • Qualitative behaviour of positive solutions of a predator-prey model: Effects of saturation
    • Du Y., and Lou Y. Qualitative behaviour of positive solutions of a predator-prey model: Effects of saturation. Proc. Roy. Soc. Edinburgh Sect. A 131 2 (2001) 321-349
    • (2001) Proc. Roy. Soc. Edinburgh Sect. A , vol.131 , Issue.2 , pp. 321-349
    • Du, Y.1    Lou, Y.2
  • 23
    • 0000130586 scopus 로고    scopus 로고
    • N by a squeezing method involving boundary blow-up solutions
    • N by a squeezing method involving boundary blow-up solutions. J. London Math. Soc. (2) 64 1 (2001) 107-124
    • (2001) J. London Math. Soc. (2) , vol.64 , Issue.1 , pp. 107-124
    • Du, Y.1    Ma, L.2
  • 24
    • 33746751924 scopus 로고    scopus 로고
    • Y. Du, J. Shi, Allee effect and bistability in a spatially heterogeneous predator-prey model, Trans. Amer. Math. Soc. (2006), in press
  • 25
    • 0037058010 scopus 로고    scopus 로고
    • Spatial heterogeneity of resources versus Lotka-Volterra dynamics
    • Hutson V., Lou Y., and Mischaikow K. Spatial heterogeneity of resources versus Lotka-Volterra dynamics. J. Differential Equations 185 (2002) 97-136
    • (2002) J. Differential Equations , vol.185 , pp. 97-136
    • Hutson, V.1    Lou, Y.2    Mischaikow, K.3
  • 26
    • 14244261388 scopus 로고    scopus 로고
    • Convergence in competition models with small diffusion coefficients
    • Hutson V., Lou Y., and Mischaikow K. Convergence in competition models with small diffusion coefficients. J. Differential Equations 211 1 (2005) 135-161
    • (2005) J. Differential Equations , vol.211 , Issue.1 , pp. 135-161
    • Hutson, V.1    Lou, Y.2    Mischaikow, K.3
  • 28
    • 84880026161 scopus 로고
    • Some characteristics of simple types of predation and parasitism
    • Holling C.S. Some characteristics of simple types of predation and parasitism. Canadian Entomologist 91 (1959) 385-398
    • (1959) Canadian Entomologist , vol.91 , pp. 385-398
    • Holling, C.S.1
  • 29
    • 0001039597 scopus 로고
    • The size of water masses containing plankton bloom
    • Kierstead H., and Slobodkin L.B. The size of water masses containing plankton bloom. J. Mar. Res. 12 (1953) 141-147
    • (1953) J. Mar. Res. , vol.12 , pp. 141-147
    • Kierstead, H.1    Slobodkin, L.B.2
  • 30
    • 84974489232 scopus 로고
    • A general monotone scheme for elliptic systems with applications to ecological models
    • Koman P., and Leung A.W. A general monotone scheme for elliptic systems with applications to ecological models. Proc. Roy. Soc. Edinburgh Sect. A 102 (1986) 315-325
    • (1986) Proc. Roy. Soc. Edinburgh Sect. A , vol.102 , pp. 315-325
    • Koman, P.1    Leung, A.W.2
  • 31
    • 33746750723 scopus 로고    scopus 로고
    • K. Kurata, J. Shi, Optimal spatial harvesting strategy and symmetry-breaking, preprint, 2005
  • 32
    • 84972537551 scopus 로고
    • Existence and uniqueness of coexistence states for the predator-prey model with diffusion: The scalar case
    • López-Gómez J., and Pardo R. Existence and uniqueness of coexistence states for the predator-prey model with diffusion: The scalar case. Differential Integral Equations 6 5 (1993) 1025-1031
    • (1993) Differential Integral Equations , vol.6 , Issue.5 , pp. 1025-1031
    • López-Gómez, J.1    Pardo, R.2
  • 33
    • 84998211051 scopus 로고
    • Pattern formation in competition-diffusion systems in nonconvex domains
    • Matano H., and Mimura M. Pattern formation in competition-diffusion systems in nonconvex domains. Publ. Res. Inst. Math. Sci. 19 (1983) 1049-1079
    • (1983) Publ. Res. Inst. Math. Sci. , vol.19 , pp. 1049-1079
    • Matano, H.1    Mimura, M.2
  • 34
    • 0141957171 scopus 로고    scopus 로고
    • Qualitative analysis of a ratio-dependent predator-prey system with diffusion
    • Pang P.Y.H., and Wang M. Qualitative analysis of a ratio-dependent predator-prey system with diffusion. Proc. Roy. Soc. Edinburgh Sect. A 133 (2003) 919-942
    • (2003) Proc. Roy. Soc. Edinburgh Sect. A , vol.133 , pp. 919-942
    • Pang, P.Y.H.1    Wang, M.2
  • 35
    • 0000694219 scopus 로고
    • Isoperimetric inequalities and their applications
    • Payne L.E. Isoperimetric inequalities and their applications. SIAM Rev. 9 (1967) 453-488
    • (1967) SIAM Rev. , vol.9 , pp. 453-488
    • Payne, L.E.1
  • 36
    • 14644406942 scopus 로고    scopus 로고
    • Positive steady states of the Holling-Tanner prey-predator model with diffusion
    • Peng R., and Wang M. Positive steady states of the Holling-Tanner prey-predator model with diffusion. Proc. Roy. Soc. Edinburgh Sect. A 135 1 (2005) 149-164
    • (2005) Proc. Roy. Soc. Edinburgh Sect. A , vol.135 , Issue.1 , pp. 149-164
    • Peng, R.1    Wang, M.2
  • 37
    • 0035976565 scopus 로고    scopus 로고
    • Effects of marine reserves on adjacent fisheries
    • Roberts C.M., et al. Effects of marine reserves on adjacent fisheries. Science 294 (2001) 1920-1923
    • (2001) Science , vol.294 , pp. 1920-1923
    • Roberts, C.M.1
  • 38
    • 0030793909 scopus 로고    scopus 로고
    • 'No-take' zones spark fisheries debate
    • Schmidt K.F. 'No-take' zones spark fisheries debate. Science 277 (1997) 489-491
    • (1997) Science , vol.277 , pp. 489-491
    • Schmidt, K.F.1
  • 39
    • 0000103723 scopus 로고    scopus 로고
    • Persistence and bifurcation of degenerate solutions
    • Shi J. Persistence and bifurcation of degenerate solutions. J. Funct. Anal. 169 2 (1999) 494-531
    • (1999) J. Funct. Anal. , vol.169 , Issue.2 , pp. 494-531
    • Shi, J.1
  • 40
    • 22444455186 scopus 로고    scopus 로고
    • On a singular nonlinear semilinear elliptic problem
    • Shi J., and Yao M. On a singular nonlinear semilinear elliptic problem. Proc. Roy. Soc. Edinburgh Sect. A 128 6 (1998) 1389-1401
    • (1998) Proc. Roy. Soc. Edinburgh Sect. A , vol.128 , Issue.6 , pp. 1389-1401
    • Shi, J.1    Yao, M.2
  • 41
    • 0009636209 scopus 로고
    • Random dispersal in theoretical populations
    • Skellam J.G. Random dispersal in theoretical populations. Biometrika 38 (1951) 196-218
    • (1951) Biometrika , vol.38 , pp. 196-218
    • Skellam, J.G.1
  • 42
    • 0141786634 scopus 로고    scopus 로고
    • Fishing the last frontier - controversies in the regulations of shrimp trawling in the high Arctic
    • Standal D. Fishing the last frontier - controversies in the regulations of shrimp trawling in the high Arctic. Marine Policy 27 (2003) 375-388
    • (2003) Marine Policy , vol.27 , pp. 375-388
    • Standal, D.1


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