메뉴 건너뛰기




Volumn 197, Issue 2, 2004, Pages 293-314

Stability of steady-state solutions to a prey-predator system with cross-diffusion

Author keywords

Cross diffusion; Hopf bifurcation; Lyapunov Schmidt reduction; Stability; Steady state solution

Indexed keywords


EID: 1342328537     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jde.2003.10.016     Document Type: Article
Times cited : (87)

References (21)
  • 1
    • 84972541997 scopus 로고
    • Dynamic theory of quasilinear parabolic equations - II. Reaction-diffusion systems
    • H. Amann, Dynamic theory of quasilinear parabolic equations - II. Reaction-diffusion systems, Differential Integral Equations 3 (1990) 13-75.
    • (1990) Differential Integral Equations , vol.3 , pp. 13-75
    • Amann, H.1
  • 2
    • 1342321640 scopus 로고
    • Hopf bifurcation in quasilinear reaction-diffusion systems
    • S. Busenberg, M. Martelli (Eds.), Claremont, CA, Lecture Notes in Mathematics, Springer, Berlin, 1991
    • H. Amann, Hopf bifurcation in quasilinear reaction-diffusion systems, in: S. Busenberg, M. Martelli (Eds.), Delay Differential Equations and Dynamical Systems, Claremont, CA, 1990, Lecture Notes in Mathematics, Vol. 1475, Springer, Berlin, 1991, pp. 53-63.
    • (1990) Delay Differential Equations and Dynamical Systems , vol.1475 , pp. 53-63
    • Amann, H.1
  • 3
    • 0038446673 scopus 로고    scopus 로고
    • Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with weak cross-diffusion
    • Y.S. Choi, R. Lui, Y. Yamada, Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with weak cross-diffusion, Discrete Contin. Dynamic Systems 9 (2003) 1993-2000.
    • (2003) Discrete Contin. Dynamic Systems , vol.9 , pp. 1993-2000
    • Choi, Y.S.1    Lui, R.2    Yamada, Y.3
  • 4
    • 1042267866 scopus 로고    scopus 로고
    • Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with strongly coupled cross-diffusion
    • Y.S. Choi, R. Lui, Y. Yamada, Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with strongly coupled cross-diffusion, Discrete Contin. Dynamic Systems 10 (2004) 719-730.
    • (2004) Discrete Contin. Dynamic Systems , vol.10 , pp. 719-730
    • Choi, Y.S.1    Lui, R.2    Yamada, Y.3
  • 6
    • 38249005979 scopus 로고
    • The principle of linearized stability for quasilinear parabolic evolution equations
    • A.-K. Drangeid, The principle of linearized stability for quasilinear parabolic evolution equations, Nonlinear Anal. TMA 13 (1989) 1091-1113.
    • (1989) Nonlinear Anal. TMA , vol.13 , pp. 1091-1113
    • Drangeid, A.-K.1
  • 7
    • 0001674774 scopus 로고    scopus 로고
    • S-shaped global bifurcation curve and Hopf bifurcation of positive solutions to a predator-prey model
    • Y. Du, Y. Lou, S-shaped global bifurcation curve and Hopf bifurcation of positive solutions to a predator-prey model, J. Differential Equations 144 (1998) 390-440.
    • (1998) J. Differential Equations , vol.144 , pp. 390-440
    • Du, Y.1    Lou, Y.2
  • 8
    • 0002317471 scopus 로고
    • Charactérisation de quelques espaces d'interpolation
    • P. Grisvard, Charactérisation de quelques espaces d'interpolation, Arch. Rational Mech. Anal. 25 (1967) 40-63.
    • (1967) Arch. Rational Mech. Anal. , vol.25 , pp. 40-63
    • Grisvard, P.1
  • 9
    • 84972514721 scopus 로고
    • Stability of singularly perturbed solutions to nonlinear diffusion systems arising in population dynamics
    • Y. Kan-on, Stability of singularly perturbed solutions to nonlinear diffusion systems arising in population dynamics, Hiroshima Math. J. 23 (1993) 509-536.
    • (1993) Hiroshima Math. J. , vol.23 , pp. 509-536
    • Kan-on, Y.1
  • 11
    • 33745099681 scopus 로고    scopus 로고
    • Multiple coexistence states for a prey-predator system with cross-diffusion
    • in press
    • K. Kuto, Y. Yamada, Multiple coexistence states for a prey-predator system with cross-diffusion, J. Differential Equations, in press.
    • J. Differential Equations
    • Kuto, K.1    Yamada, Y.2
  • 12
    • 84966242093 scopus 로고
    • Coexistence theorems of steady states for predator-prey interacting system
    • L. Li, Coexistence theorems of steady states for predator-prey interacting system, Trans. Amer. Math. Soc. 305 (1988) 143-166.
    • (1988) Trans. Amer. Math. Soc. , vol.305 , pp. 143-166
    • Li, L.1
  • 13
    • 51649142197 scopus 로고
    • Sur une classe d'espaces d'interpolation
    • J.L. Lions, J. Peetre, Sur une classe d'espaces d'interpolation, Publ. Math. IHES 19 (1964) 5-68.
    • (1964) Publ. Math. IHES , vol.19 , pp. 5-68
    • Lions, J.L.1    Peetre, J.2
  • 14
    • 38249012051 scopus 로고
    • Coexistence regions in Lotka-Volterra models with diffusion
    • J. López-Gómez, R. Pardo, Coexistence regions in Lotka-Volterra models with diffusion, Nonlinear Anal. TMA 19 (1992) 11-28.
    • (1992) Nonlinear Anal. TMA , vol.19 , pp. 11-28
    • López-Gómez, J.1    Pardo, R.2
  • 15
    • 84972537551 scopus 로고
    • Existence and uniqueness of coexistence states for the predator-prey model with diffusion
    • J. López-Gómez, R. Pardo, Existence and uniqueness of coexistence states for the predator-prey model with diffusion, Differential Integral Equations 6 (1993) 1025-1031.
    • (1993) Differential Integral Equations , vol.6 , pp. 1025-1031
    • López-Gómez, J.1    Pardo, R.2
  • 16
    • 0032388194 scopus 로고    scopus 로고
    • On the global existence of a cross-diffusion system
    • Y. Lou, W.-M. Ni, Y. Wu, On the global existence of a cross-diffusion system, Discrete Contin. Dynamic Systems 4 (1998) 193-203.
    • (1998) Discrete Contin. Dynamic Systems , vol.4 , pp. 193-203
    • Lou, Y.1    Ni, W.-M.2    Wu, Y.3
  • 17
    • 84972584509 scopus 로고
    • Coexistence problem for two competing species models with density-dependent diffusion
    • M. Mimura, Y. Nishiura, A. Tesei, T. Tsujikawa, Coexistence problem for two competing species models with density-dependent diffusion, Hiroshima Math. J. 14 (1984) 425-449.
    • (1984) Hiroshima Math. J. , vol.14 , pp. 425-449
    • Mimura, M.1    Nishiura, Y.2    Tesei, A.3    Tsujikawa, T.4
  • 18
    • 0003226269 scopus 로고    scopus 로고
    • Positive steady states for prey-predator models with cross-diffusion
    • K. Nakashima, Y. Yamada, Positive steady states for prey-predator models with cross-diffusion, Adv. Differential Equations 6 (1996) 1099-1122.
    • (1996) Adv. Differential Equations , vol.6 , pp. 1099-1122
    • Nakashima, K.1    Yamada, Y.2
  • 19
    • 1342300494 scopus 로고    scopus 로고
    • Diffusion and Ecological Problems: Modern Perspective
    • 2nd Edn. Springer, New York
    • A. Okubo, L.A. Levin, Diffusion and Ecological Problems: Modern Perspective, 2nd Edn., Interdisciplinary Applied Mathematics, Vol. 14, Springer, New York, 2001.
    • (2001) Interdisciplinary Applied Mathematics , vol.14
    • Okubo, A.1    Levin, L.A.2
  • 20
    • 0019680550 scopus 로고
    • The linearization principle for the stability of solutions of quasilinear parabolic equations - I
    • M. Potier-Ferry, The linearization principle for the stability of solutions of quasilinear parabolic equations - I, Arch. Rational Mech. Anal. 77 (1981) 301-320.
    • (1981) Arch. Rational Mech. Anal. , vol.77 , pp. 301-320
    • Potier-Ferry, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.