메뉴 건너뛰기




Volumn 186, Issue 1, 2003, Pages 79-91

An exactly solvable model of population dynamics with density-dependent migrations and the Allee effect

Author keywords

Advection; Allee effect; Biological invasion; Diffusion reaction equation; Exact solution; Migration

Indexed keywords

BIODIVERSITY; DIFFERENTIAL EQUATIONS; ENVIRONMENTAL IMPACT; MATHEMATICAL MODELS; NONLINEAR EQUATIONS;

EID: 0142053105     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0025-5564(03)00098-1     Document Type: Article
Times cited : (56)

References (35)
  • 3
    • 0024903148 scopus 로고
    • A theoretical framework for data analysis of wind dispersal of seeds and pollen
    • A. Okubo, S. Levin, A theoretical framework for data analysis of wind dispersal of seeds and pollen, Ecology 70 (1989) 329.
    • (1989) Ecology , vol.70 , pp. 329
    • Okubo, A.1    Levin, S.2
  • 4
    • 0027524391 scopus 로고
    • Allee dynamics and the spread of invading organisms
    • M.A. Lewis, P. Kareiva, Allee dynamics and the spread of invading organisms, Theor. Popul. Biol. 43 (1993) 141.
    • (1993) Theor. Popul. Biol. , vol.43 , pp. 141
    • Lewis, M.A.1    Kareiva, P.2
  • 5
    • 0030426365 scopus 로고    scopus 로고
    • Dispersal data and the spread of invading organisms
    • M. Kot, M.A. Lewis, P. van der Driessche, Dispersal data and the spread of invading organisms, Ecology 77 (1996) 2027.
    • (1996) Ecology , vol.77 , pp. 2027
    • Kot, M.1    Lewis, M.A.2    Van der Driessche, P.3
  • 7
    • 0034895545 scopus 로고    scopus 로고
    • How predation can slow, stop or reverse a prey invasion
    • M.R. Owen, M.A. Lewis, How predation can slow, stop or reverse a prey invasion, Bull. Math. Biol. 63 (2001) 655.
    • (2001) Bull. Math. Biol. , vol.63 , pp. 655
    • Owen, M.R.1    Lewis, M.A.2
  • 8
    • 0034846910 scopus 로고    scopus 로고
    • Some exact solutions of a generalized Fisher equation related to the problem of biological invasion
    • S.V. Petrovskii, N. Shigesada, Some exact solutions of a generalized Fisher equation related to the problem of biological invasion, Math. Biosci. 172 (2001) 73.
    • (2001) Math. Biosci. , vol.172 , pp. 73
    • Petrovskii, S.V.1    Shigesada, N.2
  • 9
    • 21944457273 scopus 로고    scopus 로고
    • Localization of a nonlinear switching wave in an active medium with an isolated inhomogeneity
    • S.V. Petrovskii, Localization of a nonlinear switching wave in an active medium with an isolated inhomogeneity, Tech. Phys. 42 (1997) 866.
    • (1997) Tech. Phys. , vol.42 , pp. 866
    • Petrovskii, S.V.1
  • 10
    • 0032860454 scopus 로고    scopus 로고
    • On the plankton front waves accelerated by marine turbulence
    • S.V. Petrovskii, On the plankton front waves accelerated by marine turbulence, J. Mar. Syst. 21 (1999) 179.
    • (1999) J. Mar. Syst. , vol.21 , pp. 179
    • Petrovskii, S.V.1
  • 12
    • 0028978462 scopus 로고
    • Modelling stratified diffusion in biological invasions
    • N. Shigesada, K. Kawasaki, Y. Takeda, Modelling stratified diffusion in biological invasions, Am. Nat. 146 (1995) 229.
    • (1995) Am. Nat. , vol.146 , pp. 229
    • Shigesada, N.1    Kawasaki, K.2    Takeda, Y.3
  • 13
    • 0018569774 scopus 로고
    • Explicit solutions of Fisher's equations for a special wave speed
    • M.J. Ablowitz, A. Zeppetella, Explicit solutions of Fisher's equations for a special wave speed, Bull. Math. Biol. 41 (1979) 835.
    • (1979) Bull. Math. Biol. , vol.41 , pp. 835
    • Ablowitz, M.J.1    Zeppetella, A.2
  • 14
    • 36749119273 scopus 로고
    • A symmetry approach to exactly solvable evolution equations
    • A.S. Fokas, A symmetry approach to exactly solvable evolution equations, J. Math. Phys. 21 (1980) 1318.
    • (1980) J. Math. Phys. , vol.21 , pp. 1318
    • Fokas, A.S.1
  • 15
    • 0018944419 scopus 로고
    • Some exact solutions to a nonlinear diffusion problem in population genetics and combustion
    • W.I. Newman, Some exact solutions to a nonlinear diffusion problem in population genetics and combustion, J. Theor. Biol. 85 (1980) 325.
    • (1980) J. Theor. Biol. , vol.85 , pp. 325
    • Newman, W.I.1
  • 17
    • 0001068194 scopus 로고
    • Interactions of travelling fronts: An exact solution of a nonlinear diffusion equation
    • T. Kawahara, M. Tanaka, Interactions of travelling fronts: an exact solution of a nonlinear diffusion equation, Phys. Lett. A 97 (1983) 311.
    • (1983) Phys. Lett. A , vol.97 , pp. 311
    • Kawahara, T.1    Tanaka, M.2
  • 18
    • 0043176833 scopus 로고
    • Singular manifold equations and exact solutions for some nonlinear partial differential equations
    • N.A. Kudryashov, Singular manifold equations and exact solutions for some nonlinear partial differential equations, Phys. Lett. A 182 (1993) 356.
    • (1993) Phys. Lett. A , vol.182 , pp. 356
    • Kudryashov, N.A.1
  • 19
    • 21844494438 scopus 로고
    • Dynamics of formation of a switching wave in a dissipative bistable medium
    • M.V. Ognev, S.V. Petrovskii, V.M. Prostokishin, Dynamics of formation of a switching wave in a dissipative bistable medium, Tech. Phys. 40 (1995) 521.
    • (1995) Tech. Phys. , vol.40 , pp. 521
    • Ognev, M.V.1    Petrovskii, S.V.2    Prostokishin, V.M.3
  • 20
    • 0001199741 scopus 로고
    • C-integrable nonlinear partial differential equations
    • F. Calogero, J. Xiaoda, C-integrable nonlinear partial differential equations, J. Math. Phys. 32 (1991) 875.
    • (1991) J. Math. Phys. , vol.32 , pp. 875
    • Calogero, F.1    Xiaoda, J.2
  • 22
    • 0000604313 scopus 로고
    • Allee effects: Population growth, critical density, and the chance of extinction
    • B. Dennis, Allee effects: population growth, critical density, and the chance of extinction, Nat. Res. Model. 3 (1989) 481.
    • (1989) Nat. Res. Model. , vol.3 , pp. 481
    • Dennis, B.1
  • 23
    • 0009636209 scopus 로고
    • Random dispersal in theoretical populations
    • J.G. Skellam, Random dispersal in theoretical populations, Biometrika 38 (1951) 196.
    • (1951) Biometrika , vol.38 , pp. 196
    • Skellam, J.G.1
  • 24
    • 0003334526 scopus 로고
    • Diffusion and ecological problems: Mathematical models
    • Springer, Berlin
    • A. Okubo, Diffusion and ecological problems: mathematical models, in: Biomathematics, vol. 10, Springer, Berlin, 1980.
    • (1980) Biomathematics , vol.10
    • Okubo, A.1
  • 25
    • 0028176208 scopus 로고
    • Partial differential equations in ecology: Spatial interactions and population dynamics
    • E.E. Holmes, M.A. Lewis, J.E. Banks, R.R. Veit, Partial differential equations in ecology: spatial interactions and population dynamics, Ecology 75 (1994) 17.
    • (1994) Ecology , vol.75 , pp. 17
    • Holmes, E.E.1    Lewis, M.A.2    Banks, J.E.3    Veit, R.R.4
  • 28
    • 0347192775 scopus 로고    scopus 로고
    • Bifurcations of travelling waves in population taxis models
    • F.S. Berezovskaya, G.P. Karev, Bifurcations of travelling waves in population taxis models, Phys.-Usp. 169 (1999) 1011.
    • (1999) Phys.-Usp. , vol.169 , pp. 1011
    • Berezovskaya, F.S.1    Karev, G.P.2
  • 29
    • 0000268135 scopus 로고
    • The wave of advance of advantageous genes
    • R. Fisher, The wave of advance of advantageous genes, Ann. Eugenic. 7 (1937) 355.
    • (1937) Ann. Eugenic. , vol.7 , pp. 355
    • Fisher, R.1
  • 30
    • 0002722044 scopus 로고
    • Investigation of the equation of diffusion combined with increasing of the substance and its application to a biology problem
    • A.N. Kolmogorov, I.G. Petrovsky, N.S. Piskunov, Investigation of the equation of diffusion combined with increasing of the substance and its application to a biology problem, Bull. Moscow State Univ. Ser. A: Math. Mech. 1 (6) (1937) 1.
    • (1937) Bull. Moscow State Univ. Ser. A: Math. Mech. , vol.1 , Issue.6 , pp. 1
    • Kolmogorov, A.N.1    Petrovsky, I.G.2    Piskunov, N.S.3
  • 31
    • 0035012881 scopus 로고    scopus 로고
    • Speeds of invasion in a model with strong or weak Allee effects
    • M.-E. Wang, M. Kot, Speeds of invasion in a model with strong or weak Allee effects, Math. Biosci. 171 (2001) 83.
    • (2001) Math. Biosci. , vol.171 , pp. 83
    • Wang, M.-E.1    Kot, M.2
  • 32
    • 0142045968 scopus 로고
    • Exact single-phase and two-phase solutions for semilinear parabolic equations
    • V.G. Danilov, P.Yu. Subochev, Exact single-phase and two-phase solutions for semilinear parabolic equations, Teor. Mat. Fiz. 89 (1991) 25.
    • (1991) Teor. Mat. Fiz. , vol.89 , pp. 25
    • Danilov, V.G.1    Subochev, P.Yu.2
  • 33
    • 0033240507 scopus 로고    scopus 로고
    • Exact solutions of the forced Burgers equation
    • S.V. Petrovskii, Exact solutions of the forced Burgers equation, Tech. Phys. 44 (1999) 878.
    • (1999) Tech. Phys. , vol.44 , pp. 878
    • Petrovskii, S.V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.