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Dynamics of stochastic fractional Boussinesq equations
Permanence and extinction of non-autonomous Lotka-Volterra facultative systems with jump-diffusion
1. | Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China |
2. | School of Science, Beijing University of Civil Engineering and Architecture, Beijing, 100044, China, China |
References:
[1] |
R. B. Ash and C. A. Doléans-Dade, Probability and Measure Theory, Second edition, Harcourt/Academic Press, 2000. |
[2] |
A. Bahar and X. Mao, Stochastic delay population dynamics, Int. J. Pure Appl. Math., 11 (2004), 377-400. |
[3] |
J. Bao, X. Mao, G. Yin and C. Yuan, Competitive Lotka-Volterra population dynamics with jumps, Nonlinear Anal., 74 (2011), 6601-6616.
doi: 10.1016/j.na.2011.06.043. |
[4] |
J. Bao and C. Yuan, Stochastic population dynamics driven by Lévy noise, J. Math. Anal. Appl., 391 (2012), 363-375.
doi: 10.1016/j.jmaa.2012.02.043. |
[5] |
H. Bereketoglu and I. Győri, Global asymptotic stability in a nonautonomous Lotka-Volterra type system with infinite delay, J. Math. Anal. Appl., 210 (1997), 279-291.
doi: 10.1006/jmaa.1997.5403. |
[6] |
A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM, 1994.
doi: 10.1137/1.9781611971262. |
[7] |
S. Cheng, Stochastic population systems, Stoch. Anal. Appl., 27 (2009), 854-874.
doi: 10.1080/07362990902844348. |
[8] |
H. I. Freedman and S. Ruan, Uniform persistence in functional differential equations, J. Differential Equations, 115 (1995), 173-192.
doi: 10.1006/jdeq.1995.1011. |
[9] |
T. C. Gard, Persistence in stochastic food web models, Bull. Math. Biol., 46 (1984), 357-370.
doi: 10.1007/BF02462011. |
[10] |
T. C. Gard, Stability for multispecies population models in random environments, Nonlinear Anal., 10 (1986), 1411-1419.
doi: 10.1016/0362-546X(86)90111-2. |
[11] |
M. Gilpin and I. Hanski, Metapopulation Dynamics: Empirical and Theoretical Investigations, Academic Press, New York, 1991. |
[12] |
B. S. Goh, Stability in models of mutualism, Amer. Natur., 113 (1979), 261-275.
doi: 10.1086/283384. |
[13] |
K. Gopalsamy, Global asymptotic stability in Volterra's population systems, J. Math. Biol., 19 (1984), 157-168.
doi: 10.1007/BF00277744. |
[14] |
K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, Kluwer Academic, Dordrecht, 1992.
doi: 10.1007/978-94-015-7920-9. |
[15] |
T. G. Hallam and Z. Ma, Persistence in population models with demographic fluctuations, J. Math. Biol., 24 (1986), 327-339.
doi: 10.1007/BF00275641. |
[16] |
F. B. Hanson and H. C. Tuckwell, Persistence times of populations with large random fluctuations, Theoret. Population Biol., 14 (1978), 46-61.
doi: 10.1016/0040-5809(78)90003-5. |
[17] |
F. B. Hanson and H. C. Tuckwell, Logistic growth with random density independent disasters, Theoret. Population Biol., 19 (1981), 1-18.
doi: 10.1016/0040-5809(81)90032-0. |
[18] |
F. B. Hanson and H. C. Tuckwell, Population growth with randomly distributed jumps, J. Math. Biol., 36 (1997), 169-187.
doi: 10.1007/s002850050096. |
[19] |
X. He and K. Gopalsamy, Persistence, attractivity, and delay in facultative mutualism, J. Math. Anal. Appl., 215 (1997), 154-173.
doi: 10.1006/jmaa.1997.5632. |
[20] |
C. Ji and D. Jiang, Persistence and non-persistence of a mutualism system with stochastic perturbation, Discrete Contin. Dyn. Syst., 32 (2012), 867-889.
doi: 10.3934/dcds.2012.32.867. |
[21] |
V. Kolmanovskii and A. Myshkis, Applied Theory of Functional Differential Equations, Kluwer Academic, Dordrecht, 1992.
doi: 10.1007/978-94-015-8084-7. |
[22] |
Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, Boston, 1993. |
[23] |
Y. Kuang and H. L. Smith, Global stability for infinite delay Lotka-Valterra type systems, J. Differential Equations, 103 (1993), 221-246.
doi: 10.1006/jdeq.1993.1048. |
[24] |
R. Lande, Risks of population extinction from demographic and environmental stochasticity and random catastrophes, Amer. Natur., 142 (1993), 911-927. |
[25] |
R. Lande, Genetics and demography in biological conservation, Science, 241 (1988), 1455-1460. |
[26] |
R. Sh. Lipster, A strong law of large numbers for local martingales, Stochastics, 3 (1980), 217-228.
doi: 10.1080/17442508008833146. |
[27] |
M. Liu and K. Wang, Population dynamical behavior of Lotka-Volterra cooperative systems with random perturbations, Discrete Contin. Dyn. Syst., 33 (2013), 2495-2522.
doi: 10.3934/dcds.2013.33.2495. |
[28] |
M. Liu and K. Wang, Analysis of a stochastic autonomous mutualism model, J. Math. Anal. Appl., 402 (2013), 392-403.
doi: 10.1016/j.jmaa.2012.11.043. |
[29] |
M. Liu and K. Wang, Dynamics of a Leslie-Gower Holling-type II predator-prey system with Lévy jumps, Nonlinear Anal., 85 (2013), 204-213.
doi: 10.1016/j.na.2013.02.018. |
[30] |
X. Mao, Stochastic Differential Equations and Applications, Second edition, Horwood Publishing, Chichester, 2008.
doi: 10.1533/9780857099402. |
[31] |
X. Mao, Stationary distribution of stochastic population systems, Systems Control Lett., 60 (2011), 398-405.
doi: 10.1016/j.sysconle.2011.02.013. |
[32] |
R. M. May, Stability and Complexity in Model Ecosystems, Princeton University Press, 1974. |
[33] |
R. J. Plemmons, M-matrix characterizations. I. Nonsingular M-matrices, Linear Algebra and Appl., 18 (1977), 175-188.
doi: 10.1016/0024-3795(77)90073-8. |
[34] |
G. Poole and T. Boullion, A Survey on M-Matrices, SIAM Rev., 16 (1974), 419-427.
doi: 10.1137/1016079. |
[35] |
J. Tong, Z. Zhang and J. Bao, The stationary distribution of the facultative population model with a degenerate noise, Statist. Probab. Lett., 83 (2013), 655-664.
doi: 10.1016/j.spl.2012.11.003. |
show all references
References:
[1] |
R. B. Ash and C. A. Doléans-Dade, Probability and Measure Theory, Second edition, Harcourt/Academic Press, 2000. |
[2] |
A. Bahar and X. Mao, Stochastic delay population dynamics, Int. J. Pure Appl. Math., 11 (2004), 377-400. |
[3] |
J. Bao, X. Mao, G. Yin and C. Yuan, Competitive Lotka-Volterra population dynamics with jumps, Nonlinear Anal., 74 (2011), 6601-6616.
doi: 10.1016/j.na.2011.06.043. |
[4] |
J. Bao and C. Yuan, Stochastic population dynamics driven by Lévy noise, J. Math. Anal. Appl., 391 (2012), 363-375.
doi: 10.1016/j.jmaa.2012.02.043. |
[5] |
H. Bereketoglu and I. Győri, Global asymptotic stability in a nonautonomous Lotka-Volterra type system with infinite delay, J. Math. Anal. Appl., 210 (1997), 279-291.
doi: 10.1006/jmaa.1997.5403. |
[6] |
A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM, 1994.
doi: 10.1137/1.9781611971262. |
[7] |
S. Cheng, Stochastic population systems, Stoch. Anal. Appl., 27 (2009), 854-874.
doi: 10.1080/07362990902844348. |
[8] |
H. I. Freedman and S. Ruan, Uniform persistence in functional differential equations, J. Differential Equations, 115 (1995), 173-192.
doi: 10.1006/jdeq.1995.1011. |
[9] |
T. C. Gard, Persistence in stochastic food web models, Bull. Math. Biol., 46 (1984), 357-370.
doi: 10.1007/BF02462011. |
[10] |
T. C. Gard, Stability for multispecies population models in random environments, Nonlinear Anal., 10 (1986), 1411-1419.
doi: 10.1016/0362-546X(86)90111-2. |
[11] |
M. Gilpin and I. Hanski, Metapopulation Dynamics: Empirical and Theoretical Investigations, Academic Press, New York, 1991. |
[12] |
B. S. Goh, Stability in models of mutualism, Amer. Natur., 113 (1979), 261-275.
doi: 10.1086/283384. |
[13] |
K. Gopalsamy, Global asymptotic stability in Volterra's population systems, J. Math. Biol., 19 (1984), 157-168.
doi: 10.1007/BF00277744. |
[14] |
K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, Kluwer Academic, Dordrecht, 1992.
doi: 10.1007/978-94-015-7920-9. |
[15] |
T. G. Hallam and Z. Ma, Persistence in population models with demographic fluctuations, J. Math. Biol., 24 (1986), 327-339.
doi: 10.1007/BF00275641. |
[16] |
F. B. Hanson and H. C. Tuckwell, Persistence times of populations with large random fluctuations, Theoret. Population Biol., 14 (1978), 46-61.
doi: 10.1016/0040-5809(78)90003-5. |
[17] |
F. B. Hanson and H. C. Tuckwell, Logistic growth with random density independent disasters, Theoret. Population Biol., 19 (1981), 1-18.
doi: 10.1016/0040-5809(81)90032-0. |
[18] |
F. B. Hanson and H. C. Tuckwell, Population growth with randomly distributed jumps, J. Math. Biol., 36 (1997), 169-187.
doi: 10.1007/s002850050096. |
[19] |
X. He and K. Gopalsamy, Persistence, attractivity, and delay in facultative mutualism, J. Math. Anal. Appl., 215 (1997), 154-173.
doi: 10.1006/jmaa.1997.5632. |
[20] |
C. Ji and D. Jiang, Persistence and non-persistence of a mutualism system with stochastic perturbation, Discrete Contin. Dyn. Syst., 32 (2012), 867-889.
doi: 10.3934/dcds.2012.32.867. |
[21] |
V. Kolmanovskii and A. Myshkis, Applied Theory of Functional Differential Equations, Kluwer Academic, Dordrecht, 1992.
doi: 10.1007/978-94-015-8084-7. |
[22] |
Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, Boston, 1993. |
[23] |
Y. Kuang and H. L. Smith, Global stability for infinite delay Lotka-Valterra type systems, J. Differential Equations, 103 (1993), 221-246.
doi: 10.1006/jdeq.1993.1048. |
[24] |
R. Lande, Risks of population extinction from demographic and environmental stochasticity and random catastrophes, Amer. Natur., 142 (1993), 911-927. |
[25] |
R. Lande, Genetics and demography in biological conservation, Science, 241 (1988), 1455-1460. |
[26] |
R. Sh. Lipster, A strong law of large numbers for local martingales, Stochastics, 3 (1980), 217-228.
doi: 10.1080/17442508008833146. |
[27] |
M. Liu and K. Wang, Population dynamical behavior of Lotka-Volterra cooperative systems with random perturbations, Discrete Contin. Dyn. Syst., 33 (2013), 2495-2522.
doi: 10.3934/dcds.2013.33.2495. |
[28] |
M. Liu and K. Wang, Analysis of a stochastic autonomous mutualism model, J. Math. Anal. Appl., 402 (2013), 392-403.
doi: 10.1016/j.jmaa.2012.11.043. |
[29] |
M. Liu and K. Wang, Dynamics of a Leslie-Gower Holling-type II predator-prey system with Lévy jumps, Nonlinear Anal., 85 (2013), 204-213.
doi: 10.1016/j.na.2013.02.018. |
[30] |
X. Mao, Stochastic Differential Equations and Applications, Second edition, Horwood Publishing, Chichester, 2008.
doi: 10.1533/9780857099402. |
[31] |
X. Mao, Stationary distribution of stochastic population systems, Systems Control Lett., 60 (2011), 398-405.
doi: 10.1016/j.sysconle.2011.02.013. |
[32] |
R. M. May, Stability and Complexity in Model Ecosystems, Princeton University Press, 1974. |
[33] |
R. J. Plemmons, M-matrix characterizations. I. Nonsingular M-matrices, Linear Algebra and Appl., 18 (1977), 175-188.
doi: 10.1016/0024-3795(77)90073-8. |
[34] |
G. Poole and T. Boullion, A Survey on M-Matrices, SIAM Rev., 16 (1974), 419-427.
doi: 10.1137/1016079. |
[35] |
J. Tong, Z. Zhang and J. Bao, The stationary distribution of the facultative population model with a degenerate noise, Statist. Probab. Lett., 83 (2013), 655-664.
doi: 10.1016/j.spl.2012.11.003. |
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