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A Lotka-Volterra system with patch structure (related to a multi-group SI epidemic model)
1. | Department of Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo, 169-8555 |
References:
[1] |
N. P. Bhatia and G. P. Szegö, Dynamical Systems,, Stability Theory and Applications//Lecture Notes in Mathematics. 35. Berlin: Springer, 35 (1967).
|
[2] |
A. Berman and R. Plemmons, Nonnegative Matrices in the Mathematical Sciences,, Academic Press, (1979).
|
[3] |
F. Chen, The permanence and global attractivity of Lotka-Volterra competition system witheedback controls,, Nonlinear Anal. RWA, 7 (2006), 133.
doi: 10.1016/j.nonrwa.2005.01.006. |
[4] |
T. Faria, Asymptotic behabiour for a class of delayed cooperative models with patch structure,, Discrete and cont. Dynam. Sys. Series B, 18 (2013), 1567.
doi: 10.3934/dcdsb.2013.18.1567. |
[5] |
T. Faria, Global dynamics for Lotka-Volterra systems with infinite delay and patch structure,, Appl. Math. Comput., 245 (2014), 575.
doi: 10.1016/j.amc.2014.08.009. |
[6] |
T. Faria and Y. Muroya, Global attractivity and extinction for Lotka-Volterra systems with infinite delay and feedback controls,, Proceedings of the Royal Society of Edinburgh: Section A, 145 (2015), 301.
doi: 10.1017/S0308210513001194. |
[7] |
A. Hastings, Spatial heterogeneity and the stability of predator prey systems,, Theoret. Popul. Biol., 12 (1977), 37.
doi: 10.1016/0040-5809(77)90034-X. |
[8] |
T. Kuniya and Y. Muroya, Global stability of a multi-group SIS epidemic model for population migration,, Discrete and Continuous Dynamical Systems-Series B, 19 (2014), 1105.
doi: 10.3934/dcdsb.2014.19.1105. |
[9] |
Z. Li, M. Han and F. Chen, Influence of feedback controls on an autonomous Lotka-Volterra competitive system with infinite delays,, Nonlinear Analysis, 14 (2013), 402.
doi: 10.1016/j.nonrwa.2012.07.004. |
[10] |
Y. Muroya, Global stability of a delayed nonlinear Lotka-Volterra system with feedback controls and patch structure,, Appl. Math. Comput., 239 (2014), 60.
doi: 10.1016/j.amc.2014.04.036. |
[11] |
Y. Muroya, Y. Enatsu and T. Kuniya, Global stability of extended multi-group SIR epidemic models with patches through migration and cross patch infection,, Acta Mathematica Scientia, 33 (2013), 341.
doi: 10.1016/S0252-9602(13)60003-X. |
[12] |
Y. Muroya, T. Kuniya and J. Wang, A delayed multi-group SIS epidemic model with nonlinear incidence rates and patch structure,, J. Math. Anal. Appl., 425 (2015), 415.
doi: 10.1016/j.jmaa.2014.12.019. |
[13] |
L. Nie, J. Peng and Z. Teng, Permanence and stability in multi-species non-autonomous Lotka-Volterra competitive systems with delays and feedback controls,, Math. Comput. Modelling, 49 (2009), 295.
doi: 10.1016/j.mcm.2008.05.004. |
[14] |
C. Shi, Z. Li and F. Chen, Extinction in a nonautonomous Lotka-Volterra competitive system with infinite delay and feedback controls,, Nonlinear Analysis, 13 (2012), 2214.
doi: 10.1016/j.nonrwa.2012.01.016. |
[15] |
H. L. Smith, Monotone Dynamical Systems,, An Introduction to the Theory of Competitive and Cooperative Systems, (1995).
|
[16] |
H. L. Smith and P. Waltman, The Theory of The Chemostat,, Cambridge University Press, (1995).
doi: 10.1017/CBO9780511530043. |
[17] |
Y. Takeuchi, W. Wang and Y. Saito, Global stability of population models with patch structure,, Nonlinear Analysis RWA, 7 (2006), 235.
doi: 10.1016/j.nonrwa.2005.02.005. |
show all references
References:
[1] |
N. P. Bhatia and G. P. Szegö, Dynamical Systems,, Stability Theory and Applications//Lecture Notes in Mathematics. 35. Berlin: Springer, 35 (1967).
|
[2] |
A. Berman and R. Plemmons, Nonnegative Matrices in the Mathematical Sciences,, Academic Press, (1979).
|
[3] |
F. Chen, The permanence and global attractivity of Lotka-Volterra competition system witheedback controls,, Nonlinear Anal. RWA, 7 (2006), 133.
doi: 10.1016/j.nonrwa.2005.01.006. |
[4] |
T. Faria, Asymptotic behabiour for a class of delayed cooperative models with patch structure,, Discrete and cont. Dynam. Sys. Series B, 18 (2013), 1567.
doi: 10.3934/dcdsb.2013.18.1567. |
[5] |
T. Faria, Global dynamics for Lotka-Volterra systems with infinite delay and patch structure,, Appl. Math. Comput., 245 (2014), 575.
doi: 10.1016/j.amc.2014.08.009. |
[6] |
T. Faria and Y. Muroya, Global attractivity and extinction for Lotka-Volterra systems with infinite delay and feedback controls,, Proceedings of the Royal Society of Edinburgh: Section A, 145 (2015), 301.
doi: 10.1017/S0308210513001194. |
[7] |
A. Hastings, Spatial heterogeneity and the stability of predator prey systems,, Theoret. Popul. Biol., 12 (1977), 37.
doi: 10.1016/0040-5809(77)90034-X. |
[8] |
T. Kuniya and Y. Muroya, Global stability of a multi-group SIS epidemic model for population migration,, Discrete and Continuous Dynamical Systems-Series B, 19 (2014), 1105.
doi: 10.3934/dcdsb.2014.19.1105. |
[9] |
Z. Li, M. Han and F. Chen, Influence of feedback controls on an autonomous Lotka-Volterra competitive system with infinite delays,, Nonlinear Analysis, 14 (2013), 402.
doi: 10.1016/j.nonrwa.2012.07.004. |
[10] |
Y. Muroya, Global stability of a delayed nonlinear Lotka-Volterra system with feedback controls and patch structure,, Appl. Math. Comput., 239 (2014), 60.
doi: 10.1016/j.amc.2014.04.036. |
[11] |
Y. Muroya, Y. Enatsu and T. Kuniya, Global stability of extended multi-group SIR epidemic models with patches through migration and cross patch infection,, Acta Mathematica Scientia, 33 (2013), 341.
doi: 10.1016/S0252-9602(13)60003-X. |
[12] |
Y. Muroya, T. Kuniya and J. Wang, A delayed multi-group SIS epidemic model with nonlinear incidence rates and patch structure,, J. Math. Anal. Appl., 425 (2015), 415.
doi: 10.1016/j.jmaa.2014.12.019. |
[13] |
L. Nie, J. Peng and Z. Teng, Permanence and stability in multi-species non-autonomous Lotka-Volterra competitive systems with delays and feedback controls,, Math. Comput. Modelling, 49 (2009), 295.
doi: 10.1016/j.mcm.2008.05.004. |
[14] |
C. Shi, Z. Li and F. Chen, Extinction in a nonautonomous Lotka-Volterra competitive system with infinite delay and feedback controls,, Nonlinear Analysis, 13 (2012), 2214.
doi: 10.1016/j.nonrwa.2012.01.016. |
[15] |
H. L. Smith, Monotone Dynamical Systems,, An Introduction to the Theory of Competitive and Cooperative Systems, (1995).
|
[16] |
H. L. Smith and P. Waltman, The Theory of The Chemostat,, Cambridge University Press, (1995).
doi: 10.1017/CBO9780511530043. |
[17] |
Y. Takeuchi, W. Wang and Y. Saito, Global stability of population models with patch structure,, Nonlinear Analysis RWA, 7 (2006), 235.
doi: 10.1016/j.nonrwa.2005.02.005. |
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