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The improved results on the stochastic Kolmogorov system with time-varying delay
1. | School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China |
2. | School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074 |
References:
[1] |
A. Bahar and X. Mao, Stochastic delay Lotka-Volterra model, Journal of Mathematical Analysis and Applications, 292 (2004), 364-380.
doi: 10.1016/j.jmaa.2003.12.004. |
[2] |
A. Bahar and X. Mao, Stochastic delay population dynamics, International Journal of Pure and Applied Mathematics, 11 (2004), 377-400. |
[3] |
A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia, PA, 1994.
doi: 10.1137/1.9781611971262. |
[4] |
Y. Hu and F. Wu, Stochastic Kolmogorov-type population dynamics with infinite distributed delays, Acta Applicandae Mathematicae, 110 (2010), 1407-1428.
doi: 10.1007/s10440-009-9517-2. |
[5] |
Y. Hu and C. Huang, Lasalle method and general decay stability of stochastic neural networks with mixed delays, Journal of Applied Mathematics and Computing, 38 (2012), 257-278.
doi: 10.1007/s12190-011-0477-0. |
[6] |
Y. Hu and C. Huang, Existence results and the momentestimate for nonlocal stochastic differential equations with time-varying delay, Nonlinear Analysis, 75 (2012), 405-416.
doi: 10.1016/j.na.2011.08.042. |
[7] |
Y. Hu, F. Wu and C. Huang, Stochastic Lotka-Volterra models with multiple delays, Journal of Mathematical Analysis and Applications, 375 (2011), 42-57.
doi: 10.1016/j.jmaa.2010.08.017. |
[8] |
M. Jovanović and M. Vasilova, Dynamics of non-autonomous stochastic Gilpin-Ayala competition model with time-varying delays, Applied Mathematics and Computation, 219 (2013), 6946-6964.
doi: 10.1016/j.amc.2012.12.073. |
[9] |
X. Mao, G. Marion and E. Renshaw, Environmental noise supresses explosion in population dynamics, Stochastic Process and their Applications, 97 (2002), 95-110.
doi: 10.1016/S0304-4149(01)00126-0. |
[10] |
X. Mao and C. Yuan, Stochastic Differential Equations with Markovian Swithching, Imperial Collage Press, 2006.
doi: 10.1142/p473. |
[11] |
X. Mao, C. Yuan and J. Zhou, Stochatic differential delay equations of population dynamics, Journal of Mathematical Analysis and Applications, 304 (2005), 296-320.
doi: 10.1016/j.jmaa.2004.09.027. |
[12] |
S. Pang, F. Deng and X. Mao, Asymptotic properties of stochastic population dynamics, Dynamics of Continuous Discrete and Impulsive Systems Series A, 15 (2008), 603-620. |
[13] |
F. Wu and S. Hu, Stochastic Kolmogorov-type population dynamics with variable delay, Stochastic Models, 25 (2009), 129-150.
doi: 10.1080/15326340802646286. |
[14] |
F. Wu and Y. Xu, Stochastic Lotka-Volterra population dynamics with infinite delay, SIAM Journal on Applied Mathematics, 70 (2009), 641-657.
doi: 10.1137/080719194. |
[15] |
F. Wu, Unbounded delay stochastic functional Kolmogorov-type system, Proceedings of the Royal Society of Edinburgh: Section A, 140 (2010), 1309-1334.
doi: 10.1017/S0308210509000237. |
[16] |
F. Wu and Y. Hu, Existence and uniqueness of global positive solutions to the stochastic functional Kolmogorov-type system, IMA Journal of Applied Mathematics, 75 (2010), 317-332.
doi: 10.1093/imamat/hxq025. |
[17] |
F. Wu, S. Hu and Y. Liu, Positive solution and its asymptotic behaviour of stochastic functional Kolmogorov-type system, Journal of Mathematical Analysis and Applications, 364 (2010), 104-118.
doi: 10.1016/j.jmaa.2009.10.072. |
show all references
References:
[1] |
A. Bahar and X. Mao, Stochastic delay Lotka-Volterra model, Journal of Mathematical Analysis and Applications, 292 (2004), 364-380.
doi: 10.1016/j.jmaa.2003.12.004. |
[2] |
A. Bahar and X. Mao, Stochastic delay population dynamics, International Journal of Pure and Applied Mathematics, 11 (2004), 377-400. |
[3] |
A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia, PA, 1994.
doi: 10.1137/1.9781611971262. |
[4] |
Y. Hu and F. Wu, Stochastic Kolmogorov-type population dynamics with infinite distributed delays, Acta Applicandae Mathematicae, 110 (2010), 1407-1428.
doi: 10.1007/s10440-009-9517-2. |
[5] |
Y. Hu and C. Huang, Lasalle method and general decay stability of stochastic neural networks with mixed delays, Journal of Applied Mathematics and Computing, 38 (2012), 257-278.
doi: 10.1007/s12190-011-0477-0. |
[6] |
Y. Hu and C. Huang, Existence results and the momentestimate for nonlocal stochastic differential equations with time-varying delay, Nonlinear Analysis, 75 (2012), 405-416.
doi: 10.1016/j.na.2011.08.042. |
[7] |
Y. Hu, F. Wu and C. Huang, Stochastic Lotka-Volterra models with multiple delays, Journal of Mathematical Analysis and Applications, 375 (2011), 42-57.
doi: 10.1016/j.jmaa.2010.08.017. |
[8] |
M. Jovanović and M. Vasilova, Dynamics of non-autonomous stochastic Gilpin-Ayala competition model with time-varying delays, Applied Mathematics and Computation, 219 (2013), 6946-6964.
doi: 10.1016/j.amc.2012.12.073. |
[9] |
X. Mao, G. Marion and E. Renshaw, Environmental noise supresses explosion in population dynamics, Stochastic Process and their Applications, 97 (2002), 95-110.
doi: 10.1016/S0304-4149(01)00126-0. |
[10] |
X. Mao and C. Yuan, Stochastic Differential Equations with Markovian Swithching, Imperial Collage Press, 2006.
doi: 10.1142/p473. |
[11] |
X. Mao, C. Yuan and J. Zhou, Stochatic differential delay equations of population dynamics, Journal of Mathematical Analysis and Applications, 304 (2005), 296-320.
doi: 10.1016/j.jmaa.2004.09.027. |
[12] |
S. Pang, F. Deng and X. Mao, Asymptotic properties of stochastic population dynamics, Dynamics of Continuous Discrete and Impulsive Systems Series A, 15 (2008), 603-620. |
[13] |
F. Wu and S. Hu, Stochastic Kolmogorov-type population dynamics with variable delay, Stochastic Models, 25 (2009), 129-150.
doi: 10.1080/15326340802646286. |
[14] |
F. Wu and Y. Xu, Stochastic Lotka-Volterra population dynamics with infinite delay, SIAM Journal on Applied Mathematics, 70 (2009), 641-657.
doi: 10.1137/080719194. |
[15] |
F. Wu, Unbounded delay stochastic functional Kolmogorov-type system, Proceedings of the Royal Society of Edinburgh: Section A, 140 (2010), 1309-1334.
doi: 10.1017/S0308210509000237. |
[16] |
F. Wu and Y. Hu, Existence and uniqueness of global positive solutions to the stochastic functional Kolmogorov-type system, IMA Journal of Applied Mathematics, 75 (2010), 317-332.
doi: 10.1093/imamat/hxq025. |
[17] |
F. Wu, S. Hu and Y. Liu, Positive solution and its asymptotic behaviour of stochastic functional Kolmogorov-type system, Journal of Mathematical Analysis and Applications, 364 (2010), 104-118.
doi: 10.1016/j.jmaa.2009.10.072. |
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