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Exponential stability for a class of linear hyperbolic equations with hereditary memory
Asymptotic behaviour for a class of delayed cooperative models with patch structure
1. | Departamento de Matemática and CMAF, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal |
References:
[1] |
T. Faria, Global asymptotic behaviour for a Nicholson model with patch structure and multiple delays, Nonlinear Anal., 74 (2011), 7033-7046.
doi: 10.1016/j.na.2011.07.024. |
[2] |
T. Faria and J. J. Oliveira, Local and global stability for Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks, J. Differential Equations, 244 (2008), 1049-1079.
doi: 10.1016/j.jde.2007.12.005. |
[3] |
T. Faria and S. Trofimchuk, Positive travelling fronts for reaction-diffusion systems with distributed delay, Nonlinearity, 23 (2010), 2457-2481.
doi: 10.1088/0951-7715/23/10/006. |
[4] |
M. Fiedler, "Special Matrices and Their Applications in Numerical Mathematics," Martinus Nijhoff Publ., Dordrecht, 1986.
doi: 10.1007/978-94-009-4335-3. |
[5] |
B. Liu, Global stability of a class of delay differential systems, J. Comput. Appl. Math., 233 (2009), 217-223.
doi: 10.1016/j.cam.2009.07.024. |
[6] |
H. L. Smith, "Monotone Dynamical Systems. An Introduction to the Theory of Competitive and Cooperative Systems," Mathematical Surveys and Monographs, 41, Amer. Math. Soc., Providence, RI, 1995. |
[7] |
H. L. Smith and P. Waltman, "The Theory of the Chemostat. Dynamics of Microbial Competition," Cambridge Studies in Mathematical Biology, 13, Cambridge University Press, Cambridge, 1995.
doi: 10.1017/CBO9780511530043. |
[8] |
Y. Takeuchi, J. Cui, R. Miyazaki and Y. Saito, Permanence of delayed population model with dispersal loss, Math. Biosci., 201 (2006), 143-156.
doi: 10.1016/j.mbs.2005.12.012. |
[9] |
Y. Takeuchi, W. Wang and Y. Saito, Global stability of population models with patch structure, Nonlinear Anal. Real World Appl., 7 (2006), 235-247.
doi: 10.1016/j.nonrwa.2005.02.005. |
[10] |
W. Wang, P. Fergola and C. Tenneriello, Global attractivity of periodic solutions of population models, J. Math. Anal. Appl., 211 (1997), 498-511.
doi: 10.1006/jmaa.1997.5484. |
[11] |
X.-Q. Zhao and Z.-J. Jing, Global asymptotic behavior in some cooperative systems of functional differential equations, Cann. Appl. Math. Quart., 4 (1996), 421-444. |
show all references
References:
[1] |
T. Faria, Global asymptotic behaviour for a Nicholson model with patch structure and multiple delays, Nonlinear Anal., 74 (2011), 7033-7046.
doi: 10.1016/j.na.2011.07.024. |
[2] |
T. Faria and J. J. Oliveira, Local and global stability for Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks, J. Differential Equations, 244 (2008), 1049-1079.
doi: 10.1016/j.jde.2007.12.005. |
[3] |
T. Faria and S. Trofimchuk, Positive travelling fronts for reaction-diffusion systems with distributed delay, Nonlinearity, 23 (2010), 2457-2481.
doi: 10.1088/0951-7715/23/10/006. |
[4] |
M. Fiedler, "Special Matrices and Their Applications in Numerical Mathematics," Martinus Nijhoff Publ., Dordrecht, 1986.
doi: 10.1007/978-94-009-4335-3. |
[5] |
B. Liu, Global stability of a class of delay differential systems, J. Comput. Appl. Math., 233 (2009), 217-223.
doi: 10.1016/j.cam.2009.07.024. |
[6] |
H. L. Smith, "Monotone Dynamical Systems. An Introduction to the Theory of Competitive and Cooperative Systems," Mathematical Surveys and Monographs, 41, Amer. Math. Soc., Providence, RI, 1995. |
[7] |
H. L. Smith and P. Waltman, "The Theory of the Chemostat. Dynamics of Microbial Competition," Cambridge Studies in Mathematical Biology, 13, Cambridge University Press, Cambridge, 1995.
doi: 10.1017/CBO9780511530043. |
[8] |
Y. Takeuchi, J. Cui, R. Miyazaki and Y. Saito, Permanence of delayed population model with dispersal loss, Math. Biosci., 201 (2006), 143-156.
doi: 10.1016/j.mbs.2005.12.012. |
[9] |
Y. Takeuchi, W. Wang and Y. Saito, Global stability of population models with patch structure, Nonlinear Anal. Real World Appl., 7 (2006), 235-247.
doi: 10.1016/j.nonrwa.2005.02.005. |
[10] |
W. Wang, P. Fergola and C. Tenneriello, Global attractivity of periodic solutions of population models, J. Math. Anal. Appl., 211 (1997), 498-511.
doi: 10.1006/jmaa.1997.5484. |
[11] |
X.-Q. Zhao and Z.-J. Jing, Global asymptotic behavior in some cooperative systems of functional differential equations, Cann. Appl. Math. Quart., 4 (1996), 421-444. |
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