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Duffing-van der Pol-type oscillator systems
Dynamics of two phytoplankton species competing for light and nutrient with internal storage
1. | Department of Mathematics, National Tsing Hua University, National Center of Theoretical Science, Hsinchu 300, Taiwan |
2. | Department of Mathematics, National Tsing Hua University, Hsinchu 300 |
References:
[1] |
M. Droop, Some thoughts on nutrient limitation in algae, J. Phycol., 9 (1973), 264-272.
doi: 10.1111/j.1529-8817.1973.tb04092.x. |
[2] |
J. P. Grover, Constant- and variable-yield models of population growth: Responses to environmental variability and implications for competition, J. Theoret. Biol., 158 (1992), 409-428.
doi: 10.1016/S0022-5193(05)80707-6. |
[3] |
S.-B. Hsu, K.-S. Cheng and S. P. Hubbell, Exploitative competition of microorganism for two complementary nutrients in continuous cultures, SIAM J. Appl. Math., 41 (1981), 422-444.
doi: 10.1137/0141036. |
[4] |
S.-B. Hsu and T.-H. Hsu, Competitive exclusion of microbial species for a single-nutrient with internal storage, SIAM J. Appl. Math., 68 (2008), 1600-1617.
doi: 10.1137/070700784. |
[5] |
S.-B. Hsu, S. P. Hubbell and P. Waltman, A mathematical theory for single-nutrient competition in continuous culture of micro-organisms, SIAM J. Appl. Math., 32 (1977), 366-383.
doi: 10.1137/0132030. |
[6] |
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), 4083-4094.
doi: 10.1090/S0002-9947-96-01724-2. |
[7] |
J. Huisman and F. J. Weissing, Light limited growth and competition for light in well-mixed aquatic environments: An elementary, Ecology, 75 (1994), 507-520.
doi: 10.2307/1939554. |
[8] |
J. Huisman and F. J. Weissing, Competition for nutrients and light in a mixed water column: A theoretical analysis, Am. Nat., 146 (1995), 536-564.
doi: 10.1086/285814. |
[9] |
J. Jiang, X. Liang and X. Zhao, Saddle-point behavior for monotone semifolws and reaction-diffusion models, J. Diff. Equations, 203 (2004), 313-330.
doi: 10.1016/j.jde.2004.05.002. |
[10] |
B. Li and H. L. Smith, Global dynamics of microbial competition for two resources with internal storage, J. Math. Biol., 55 (2007), 481-515.
doi: 10.1007/s00285-007-0092-8. |
[11] |
J. Passarge, S. Hol, M. Escher and J. Huisman, Competition for nutrients and light: Stable coexistence, alternative stable states, or competitive exclusion?, Ecological Monographs, 76 (2006), 57-72.
doi: 10.1890/04-1824. |
[12] |
H. L. Smith and H. R. Thieme, Stable coexistence and bi-stablility for competitive systems on ordered Banach spaces, J. Diff. Equations, 176 (2001), 195-222.
doi: 10.1006/jdeq.2001.3981. |
[13] |
H. L. Smith and P. Waltman, The Theory of the Chemostat, Cambridge University Press, 1995.
doi: 10.1017/CBO9780511530043. |
[14] |
D. Tilman, Resource Competition and Community Structure, Princeton University Press, New Jersey, 1982. |
[15] |
K. Yoshiyama, J. P. Mellard, E. Litchman and C. A. Klausmeier, Phytoplankton competition for nutrients and light in a statified water column, Am. Nat., 174 (2009), 190-203.
doi: 10.1086/600113. |
[16] |
X.-Q. Zhao, Dynamical Systems in Population Biology, Springer-Verlag, New York, 2003.
doi: 10.1007/978-0-387-21761-1. |
show all references
References:
[1] |
M. Droop, Some thoughts on nutrient limitation in algae, J. Phycol., 9 (1973), 264-272.
doi: 10.1111/j.1529-8817.1973.tb04092.x. |
[2] |
J. P. Grover, Constant- and variable-yield models of population growth: Responses to environmental variability and implications for competition, J. Theoret. Biol., 158 (1992), 409-428.
doi: 10.1016/S0022-5193(05)80707-6. |
[3] |
S.-B. Hsu, K.-S. Cheng and S. P. Hubbell, Exploitative competition of microorganism for two complementary nutrients in continuous cultures, SIAM J. Appl. Math., 41 (1981), 422-444.
doi: 10.1137/0141036. |
[4] |
S.-B. Hsu and T.-H. Hsu, Competitive exclusion of microbial species for a single-nutrient with internal storage, SIAM J. Appl. Math., 68 (2008), 1600-1617.
doi: 10.1137/070700784. |
[5] |
S.-B. Hsu, S. P. Hubbell and P. Waltman, A mathematical theory for single-nutrient competition in continuous culture of micro-organisms, SIAM J. Appl. Math., 32 (1977), 366-383.
doi: 10.1137/0132030. |
[6] |
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), 4083-4094.
doi: 10.1090/S0002-9947-96-01724-2. |
[7] |
J. Huisman and F. J. Weissing, Light limited growth and competition for light in well-mixed aquatic environments: An elementary, Ecology, 75 (1994), 507-520.
doi: 10.2307/1939554. |
[8] |
J. Huisman and F. J. Weissing, Competition for nutrients and light in a mixed water column: A theoretical analysis, Am. Nat., 146 (1995), 536-564.
doi: 10.1086/285814. |
[9] |
J. Jiang, X. Liang and X. Zhao, Saddle-point behavior for monotone semifolws and reaction-diffusion models, J. Diff. Equations, 203 (2004), 313-330.
doi: 10.1016/j.jde.2004.05.002. |
[10] |
B. Li and H. L. Smith, Global dynamics of microbial competition for two resources with internal storage, J. Math. Biol., 55 (2007), 481-515.
doi: 10.1007/s00285-007-0092-8. |
[11] |
J. Passarge, S. Hol, M. Escher and J. Huisman, Competition for nutrients and light: Stable coexistence, alternative stable states, or competitive exclusion?, Ecological Monographs, 76 (2006), 57-72.
doi: 10.1890/04-1824. |
[12] |
H. L. Smith and H. R. Thieme, Stable coexistence and bi-stablility for competitive systems on ordered Banach spaces, J. Diff. Equations, 176 (2001), 195-222.
doi: 10.1006/jdeq.2001.3981. |
[13] |
H. L. Smith and P. Waltman, The Theory of the Chemostat, Cambridge University Press, 1995.
doi: 10.1017/CBO9780511530043. |
[14] |
D. Tilman, Resource Competition and Community Structure, Princeton University Press, New Jersey, 1982. |
[15] |
K. Yoshiyama, J. P. Mellard, E. Litchman and C. A. Klausmeier, Phytoplankton competition for nutrients and light in a statified water column, Am. Nat., 174 (2009), 190-203.
doi: 10.1086/600113. |
[16] |
X.-Q. Zhao, Dynamical Systems in Population Biology, Springer-Verlag, New York, 2003.
doi: 10.1007/978-0-387-21761-1. |
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