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Tribute to our friend and colleague Jean Mawhin
On a property of a generalized Kolmogorov population model
| 1. | Department of Mathematics, University of Texas at San Antonio, San Antonio, Texas 78249, United States |
| 2. | Department of Mathematics, University of Miami, Coral Gables, Miami, Florida 33124, United States |
References:
| [1] |
S. Ahmad and A. C. Lazer, Average growth and total permanence in a competitive Lotka-Volterra system, Ann. Mat. Pura Appl., 185 (2006), S47-S67.
doi: 10.1007/s10231-004-0136-2. |
| [2] |
C. Cosner and R. S. Cantrell, "Spatial Ecology via Reaction-Diffusion Equations," John Wiley, 2003. |
| [3] |
K. P. Hadeler and D. Glas, Quasimonotone systems and convergence to equilibrium in a population genetic model, J. Math. Anal. Appl., 95 (1983), 297-303.
doi: 10.1016/0022-247X(83)90108-7. |
| [4] |
M. W. Hirsch, The dynamical systems approach to differential equations, Bull. Amer. Math. Soc., 11 (1984), 1-64.
doi: 10.1090/S0273-0979-1984-15236-4. |
| [5] |
J. Jiang, Attractors for strictly monotone flows, J. Math. Anal. Appl., 162 (1991), 210-223.
doi: 10.1016/0022-247X(91)90188-6. |
| [6] |
A. N. Kolmogorov, "Sulla Teoria Di Volterra Della Lotta Per L'esistenza," Giorn. Instituto Ital. Attuari, 1936. |
| [7] |
H. L. Smith, "Monotone Dynamical Systems: An introduction to the Theory of Competitive and Cooperative Systems," Mathematical Surveys and Monographs, 41, 1995. |
| [8] |
F. Zanolin, Permanence and positive periodic solutions for Kolmogorov competing species systems, Results Math., 21 (1992), 224-250. |
| [9] |
M. L. Zeeman, Hopf bifurcation in competitive three-dimensional Lotka-Volterra systems, Dynam. Stability Syst., 8 (1993), 189-216.
doi: 10.1080/02681119308806158. |
show all references
References:
| [1] |
S. Ahmad and A. C. Lazer, Average growth and total permanence in a competitive Lotka-Volterra system, Ann. Mat. Pura Appl., 185 (2006), S47-S67.
doi: 10.1007/s10231-004-0136-2. |
| [2] |
C. Cosner and R. S. Cantrell, "Spatial Ecology via Reaction-Diffusion Equations," John Wiley, 2003. |
| [3] |
K. P. Hadeler and D. Glas, Quasimonotone systems and convergence to equilibrium in a population genetic model, J. Math. Anal. Appl., 95 (1983), 297-303.
doi: 10.1016/0022-247X(83)90108-7. |
| [4] |
M. W. Hirsch, The dynamical systems approach to differential equations, Bull. Amer. Math. Soc., 11 (1984), 1-64.
doi: 10.1090/S0273-0979-1984-15236-4. |
| [5] |
J. Jiang, Attractors for strictly monotone flows, J. Math. Anal. Appl., 162 (1991), 210-223.
doi: 10.1016/0022-247X(91)90188-6. |
| [6] |
A. N. Kolmogorov, "Sulla Teoria Di Volterra Della Lotta Per L'esistenza," Giorn. Instituto Ital. Attuari, 1936. |
| [7] |
H. L. Smith, "Monotone Dynamical Systems: An introduction to the Theory of Competitive and Cooperative Systems," Mathematical Surveys and Monographs, 41, 1995. |
| [8] |
F. Zanolin, Permanence and positive periodic solutions for Kolmogorov competing species systems, Results Math., 21 (1992), 224-250. |
| [9] |
M. L. Zeeman, Hopf bifurcation in competitive three-dimensional Lotka-Volterra systems, Dynam. Stability Syst., 8 (1993), 189-216.
doi: 10.1080/02681119308806158. |
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