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Volumn 67, Issue 5, 2007, Pages 1479-1503

Stationary pattern of a ratio-dependent food chain model with diffusion

Author keywords

Diffusion; Food chain model; Ratio dependent functional response; Stationary pattern; Steady state solution; Turing pattern

Indexed keywords

FOOD CHAIN MODEL; RATIO-DEPENDENT FUNCTIONAL RESPONSE; STATIONARY PATTERN; STEADY STATE SOLUTION;

EID: 35348966287     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/05064624X     Document Type: Article
Times cited : (86)

References (37)
  • 1
    • 0034255819 scopus 로고    scopus 로고
    • The nature of predation: Prey dependent, ratio dependent or neither?
    • P. ABRAMS AND L. GINZBURG, The nature of predation: Prey dependent, ratio dependent or neither?, Trends Ecol. Evol., 15 (2000), pp. 337-341.
    • (2000) Trends Ecol. Evol , vol.15 , pp. 337-341
    • ABRAMS, P.1    GINZBURG, L.2
  • 2
    • 0036141801 scopus 로고    scopus 로고
    • Mutual interference between predators can give rise to Turing spatial patterns
    • D. ALONSO, F. BARTUMEUS, AND J. CATALAN, Mutual interference between predators can give rise to Turing spatial patterns, Ecology, 83 (2002), pp. 28-34.
    • (2002) Ecology , vol.83 , pp. 28-34
    • ALONSO, D.1    BARTUMEUS, F.2    CATALAN, J.3
  • 3
    • 0038778726 scopus 로고
    • Global bifurcation in the Brusselator system
    • K. J, BROWN AND F. A. DAVIDSON, Global bifurcation in the Brusselator system, Nonlinear Anal., 24 (1995), pp. 1713-1725.
    • (1995) Nonlinear Anal , vol.24 , pp. 1713-1725
    • BROWN, K.J.1    DAVIDSON, F.A.2
  • 4
    • 0346072299 scopus 로고    scopus 로고
    • Pattern formation in three-dimensional reaction-diffusion systems
    • T. K. CALLAHAN AND E. KNOBLOCH, Pattern formation in three-dimensional reaction-diffusion systems, Phys. D, 132 (1999), pp. 339-362.
    • (1999) Phys. D , vol.132 , pp. 339-362
    • CALLAHAN, T.K.1    KNOBLOCH, E.2
  • 5
    • 0000013771 scopus 로고    scopus 로고
    • Extinction of top predator in a three-level food-chain model
    • C. H. CHIU AND S. B. HSU, Extinction of top predator in a three-level food-chain model, J. Math. Biol., 37 (1998), pp. 372-380.
    • (1998) J. Math. Biol , vol.37 , pp. 372-380
    • CHIU, C.H.1    HSU, S.B.2
  • 6
    • 0001842649 scopus 로고
    • Large time behavior of solutions of systems of nonlinear reaction-diffusion equations
    • E. CONWAY, D. HOFF, AND J. SMOLLER, Large time behavior of solutions of systems of nonlinear reaction-diffusion equations, SIAM J. Appl. Math., 35 (1978), pp. 1-16.
    • (1978) SIAM J. Appl. Math , vol.35 , pp. 1-16
    • CONWAY, E.1    HOFF, D.2    SMOLLER, J.3
  • 7
    • 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 Sect. A, 130 (2000), pp. 507-516.
    • (2000) Proc. Roy. Soc. Edinburgh Sect. A , vol.130 , pp. 507-516
    • DAVIDSON, F.A.1    RYNNE, B.P.2
  • 8
    • 23044527512 scopus 로고    scopus 로고
    • Qualitative behavior of positive solutions of a predator-prey model: Effects of saturation
    • Y. H. DU AND Y. LOU, Qualitative behavior of positive solutions of a predator-prey model: Effects of saturation, Proc. Roy. Soc. Edinburgh Sect. A, 131 (2001), pp. 321-349.
    • (2001) Proc. Roy. Soc. Edinburgh Sect. A , vol.131 , pp. 321-349
    • DU, Y.H.1    LOU, Y.2
  • 9
    • 0017407813 scopus 로고
    • Mathematical analysis of some three-species food-chain models
    • H. I. FREEDMAN AND P. WALTMAN, Mathematical analysis of some three-species food-chain models, Math. Biosci., 33 (1977), pp. 257-277.
    • (1977) Math. Biosci , vol.33 , pp. 257-277
    • FREEDMAN, H.I.1    WALTMAN, P.2
  • 10
    • 0019405577 scopus 로고
    • Generation of biological patterns and form: Some physical, mathematical and logical aspects
    • A. GIERER, Generation of biological patterns and form: Some physical, mathematical and logical aspects, Prog. Biophys. Biol., 37 (1981), pp. 1-47.
    • (1981) Prog. Biophys. Biol , vol.37 , pp. 1-47
    • GIERER, A.1
  • 11
    • 0025956240 scopus 로고
    • Chaos in a three-species food chain
    • A. HASTINGS, T, POWELL, AND S. B. HSU, Chaos in a three-species food chain, Ecology, 72 (1991), pp. 896-903.
    • (1991) Ecology , vol.72 , pp. 896-903
    • HASTINGS, A.1    POWELL, T.2    HSU, S.B.3
  • 12
    • 0039978016 scopus 로고
    • Geometric Theory of Semilinear Parabolic Equations
    • Springer-Verlag, Berlin, New York
    • D. HENRY, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math. 840, Springer-Verlag, Berlin, New York, 1993.
    • (1993) Lecture Notes in Math , vol.840
    • HENRY, D.1
  • 13
    • 0037210844 scopus 로고    scopus 로고
    • A ratio-dependent food chain model and its applications to biological control
    • S. B. HSU, T. W. HWANG, AND Y. KUANG, A ratio-dependent food chain model and its applications to biological control, Math. Biosci., 181 (2003), pp. 55-83.
    • (2003) Math. Biosci , vol.181 , pp. 55-83
    • HSU, S.B.1    HWANG, T.W.2    KUANG, Y.3
  • 14
    • 21444453892 scopus 로고    scopus 로고
    • Competitive exclusion and coexistence for competitive systems on ordered Banach spaces
    • S. B. HSU, H. L. SMITH, AND P. WALTMAN, Competitive exclusion and coexistence for competitive systems on ordered Banach spaces, Trans. Amer. Math. Soc., 348 (1996), pp. 4083-4094.
    • (1996) Trans. Amer. Math. Soc , vol.348 , pp. 4083-4094
    • HSU, S.B.1    SMITH, H.L.2    WALTMAN, P.3
  • 15
    • 0034652878 scopus 로고    scopus 로고
    • Existence and instability of Neumann layer solutions for a Z-component Lotka Volterra model with diffusion
    • Y. KAN-ON, Existence and instability of Neumann layer solutions for a Z-component Lotka Volterra model with diffusion, J. Math. Anal. Appl., 243 (2000), pp. 357-372.
    • (2000) J. Math. Anal. Appl , vol.243 , pp. 357-372
    • KAN-ON, Y.1
  • 16
    • 0032389543 scopus 로고    scopus 로고
    • Singular perturbation approach to a 3-component reactiondiffusion system arising in population dynamics
    • Y. KAN-ON AND M. MLMURA, Singular perturbation approach to a 3-component reactiondiffusion system arising in population dynamics, SIAM J. Math. Anal., 29 (1998), pp. 1519-1536.
    • (1998) SIAM J. Math. Anal , vol.29 , pp. 1519-1536
    • KAN-ON, Y.1    MLMURA, M.2
  • 17
    • 0028161492 scopus 로고
    • Chaos in one-predator, two-prey models: General results from bifurcation theory
    • A. KLEBANOFF AND A. HASTINGS, Chaos in one-predator, two-prey models: General results from bifurcation theory, Math. Biosci., 122 (1994), pp. 221-233.
    • (1994) Math. Biosci , vol.122 , pp. 221-233
    • KLEBANOFF, A.1    HASTINGS, A.2
  • 18
    • 0038823713 scopus 로고    scopus 로고
    • Pattern formation in a simple chemical system with general orders of autocatalysis and decay. I. Stability analysis
    • J. A. LEACH AND J. C. WEI, Pattern formation in a simple chemical system with general orders of autocatalysis and decay. I. Stability analysis, Phys. D, 180 (2003), pp. 185-209.
    • (2003) Phys. D , vol.180 , pp. 185-209
    • LEACH, J.A.1    WEI, J.C.2
  • 19
    • 0002542873 scopus 로고
    • Large amplitude stationary solutions to a Chemotaxis system
    • C. S. LIN, W. M. NI, AND I. TAKAGI, Large amplitude stationary solutions to a Chemotaxis system, J. Differential Equations, 72 (1988), pp. 1-27.
    • (1988) J. Differential Equations , vol.72 , pp. 1-27
    • LIN, C.S.1    NI, W.M.2    TAKAGI, I.3
  • 20
    • 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 (2000), pp. 175-190.
    • (2000) Discrete Contin. Dyn. Syst , vol.6 , pp. 175-190
    • LOU, Y.1    MARTINEZ, S.2    NI, W.M.3
  • 21
    • 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), pp. 157-190.
    • (1999) J. Differential Equations , vol.154 , pp. 157-190
    • LOU, Y.1    NI, W.M.2
  • 22
    • 0008827179 scopus 로고
    • Pattern formation in coupled reaction-diffusion systems
    • M. MIMURA AND Y. NISHIURA, Pattern formation in coupled reaction-diffusion systems, Japan J. Indust. Appl. Math., 12 (1995), pp. 385-424.
    • (1995) Japan J. Indust. Appl. Math , vol.12 , pp. 385-424
    • MIMURA, M.1    NISHIURA, Y.2
  • 23
    • 0001548639 scopus 로고
    • On the Neumann problem for some semilinear elliptic equations and systems of activator-inhibitor type
    • W. M. NI AND I. TAKAGI, On the Neumann problem for some semilinear elliptic equations and systems of activator-inhibitor type, Trans. Amer. Math. Soc., 297 (1986), pp. 351-368.
    • (1986) Trans. Amer. Math. Soc , vol.297 , pp. 351-368
    • NI, W.M.1    TAKAGI, I.2
  • 24
    • 30344464119 scopus 로고    scopus 로고
    • On positive solutions concentrating on spheres for the Gierer-Meinhardt system
    • W. M. NI AND J. C. WEI, On positive solutions concentrating on spheres for the Gierer-Meinhardt system, J. Differential Equations, 221 (2006), pp. 158-189.
    • (2006) J. Differential Equations , vol.221 , pp. 158-189
    • NI, W.M.1    WEI, J.C.2
  • 26
    • 0037671486 scopus 로고    scopus 로고
    • Pattern formation in spatially heterogeneous Turing reaction-diffusion models
    • K. PAGE, P. K. MAINI, AND N. A. M. MONK, Pattern formation in spatially heterogeneous Turing reaction-diffusion models, Phys. D, 181 (2003), pp. 80-101.
    • (2003) Phys. D , vol.181 , pp. 80-101
    • PAGE, K.1    MAINI, P.K.2    MONK, N.A.M.3
  • 27
    • 1442279582 scopus 로고    scopus 로고
    • Non-constant positive steady states of a predator-prey system with non-monotonic functional response and diffusion
    • P. Y. H. PANG AND M. X. WANG, Non-constant positive steady states of a predator-prey system with non-monotonic functional response and diffusion, Proc London Math. Soc. (3), 88 (2004), pp. 135-157.
    • (2004) Proc London Math. Soc , vol.88 , Issue.3 , pp. 135-157
    • PANG, P.Y.H.1    WANG, M.X.2
  • 28
    • 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 Sect. A, 133 (2003), pp. 919-942.
    • (2003) Proc. Roy. Soc. Edinburgh Sect. A , vol.133 , pp. 919-942
    • PANG, P.Y.H.1    WANG, M.X.2
  • 29
    • 0346340796 scopus 로고    scopus 로고
    • Positive steady-state solutions of the Noyes-Field model for Belousov-Zhabotinskii reaction
    • R. PENG AND M. X. WANG, Positive steady-state solutions of the Noyes-Field model for Belousov-Zhabotinskii reaction, Nonlinear Anal., 56 (2004), pp. 451-464.
    • (2004) Nonlinear Anal , vol.56 , pp. 451-464
    • PENG, R.1    WANG, M.X.2
  • 30
    • 22144487744 scopus 로고    scopus 로고
    • Pattern formation in the Brusselator system
    • R. PENG AND M. X. WANG, Pattern formation in the Brusselator system, J. Math. Anal. Appl., 309 (2005), pp. 151-166.
    • (2005) J. Math. Anal. Appl , vol.309 , pp. 151-166
    • PENG, R.1    WANG, M.X.2
  • 31
    • 14644406942 scopus 로고    scopus 로고
    • Positive steady-states of the Holling-Tanner prey-predator model with diffusion
    • R. PENG AND M. X. WANG, Positive steady-states of the Holling-Tanner prey-predator model with diffusion, Proc. Roy. Soc. Edinburgh Sect. A, 135 (2005), pp. 149-164.
    • (2005) Proc. Roy. Soc. Edinburgh Sect. A , vol.135 , pp. 149-164
    • PENG, R.1    WANG, M.X.2
  • 32
    • 34547176335 scopus 로고    scopus 로고
    • On pattern formation in the Gray-Scott model
    • R. PENG AND M. X. WANG, On pattern formation in the Gray-Scott model, Sci. China Ser. A, 50 (2007), pp. 377-386.
    • (2007) Sci. China Ser. A , vol.50 , pp. 377-386
    • PENG, R.1    WANG, M.X.2
  • 33
    • 0015243940 scopus 로고
    • Paradox of enrichment: Destabilization of exploitation systems in ecological time
    • M. L. ROSENZWEIG, Paradox of enrichment: Destabilization of exploitation systems in ecological time, Science, 171 (1969), pp. 385-387.
    • (1969) Science , vol.171 , pp. 385-387
    • ROSENZWEIG, M.L.1
  • 34
  • 35
    • 0037845132 scopus 로고    scopus 로고
    • Non-constant positive steady states of the Sel'kov model
    • M. X. WANG, Non-constant positive steady states of the Sel'kov model, J. Differential Equations, 190 (2003), pp. 600-620.
    • (2003) J. Differential Equations , vol.190 , pp. 600-620
    • WANG, M.X.1
  • 36
    • 3242888035 scopus 로고    scopus 로고
    • Stationary patterns for a prey-predator model with prey-dependent and ratio-dependent functional responses and diffusion
    • M. X. WANG, Stationary patterns for a prey-predator model with prey-dependent and ratio-dependent functional responses and diffusion, Phys. D, 196 (2004), pp. 172-192.
    • (2004) Phys. D , vol.196 , pp. 172-192
    • WANG, M.X.1
  • 37
    • 0037367343 scopus 로고    scopus 로고
    • Existence and stability of multiple-spot solutions for the Gray-Scott model in R2
    • J. C. WEI AND M. WINTER, Existence and stability of multiple-spot solutions for the Gray-Scott model in R2, Phys. D, 176 (2003), pp. 147-180.
    • (2003) Phys. D , vol.176 , pp. 147-180
    • WEI, J.C.1    WINTER, M.2


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