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Stability of a positive equilibrium state for a stochastically perturbed mathematical model of glassy-winged sharpshooter population
| 1. | Department of Higher Mathematics, Donetsk State University of Management, Chelyuskintsev str., 163-a, Donetsk, 83015 |
References:
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M. Bandyopadhyay and J. Chattopadhyay, Ratio dependent predator-prey model: Effect of environmental fluctuation and stability, Nonlinearity, 18 (2005), 913-936.
doi: 10.1088/0951-7715/18/2/022. |
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E. Beretta, V. Kolmanovskii and L. Shaikhet, Stability of epidemic model with time delays influenced by stochastic perturbations, Mathematics and Computers in Simulation (Special Issue "Delay Systems"), 45 (1998), 269-277.
doi: 10.1016/S0378-4754(97)00106-7. |
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N. Bradul and L. Shaikhet, Stability of the positive point of equilibrium of Nicholson's blowflies equation with stochastic perturbations: Numerical analysis, Discrete Dynamics in Nature and Society, 2007 (2007), 25 pp.
doi: 10.1155/2007/92959. |
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M. Carletti, On the stability properties of a stochastic model for phage-bacteria interaction in open marine environment, Mathematical Biosciences, 175 (2002), 117-131.
doi: 10.1016/S0025-5564(01)00089-X. |
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I. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations, Springer-Verlag, Berlin, 1972. |
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M. Jovanovic and M. Krstic, Stochastically perturbed vector-borne disease models with direct transmission, Applied Mathematical Modelling, 36 (2012), 5214-5228.
doi: 10.1016/j.apm.2011.11.087. |
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B. Mukhopadhyay and R. Bhattacharyya, A nonlinear mathematical model of virus-tumor-immune system interaction: Deterministic and stochastic analysis, Stochastic Analysis and Applications, 27 (2009), 409-429.
doi: 10.1080/07362990802679067. |
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R. R. Sarkar and S. Banerjee, Cancer self remission and tumor stability - a stochastic approach, Mathematical Biosciences, 196 (2005), 65-81.
doi: 10.1016/j.mbs.2005.04.001. |
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L. Shaikhet, Lyapunov Functionals and Stability of Stochastic Difference Equations, Springer, London, Dordrecht, Heidelberg, New York, 2011.
doi: 10.1007/978-0-85729-685-6. |
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L. Shaikhet, Lyapunov Functionals and Stability of Stochastic Functional Differential Equations, Springer, Dordrecht, Heidelberg, New York, London, 2013.
doi: 10.1007/978-3-319-00101-2. |
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J. Yoon, V. Hrynkiv, L. Morano A. Nguyen, S. Wilder and F. Mitchell, Mathematical modeling of Glassy-winged sharpshooter population, Mathematical Biosciences and Engineering, 11 (2014), 667-677.
doi: 10.3934/mbe.2014.11.667. |
show all references
References:
| [1] |
M. Bandyopadhyay and J. Chattopadhyay, Ratio dependent predator-prey model: Effect of environmental fluctuation and stability, Nonlinearity, 18 (2005), 913-936.
doi: 10.1088/0951-7715/18/2/022. |
| [2] |
E. Beretta, V. Kolmanovskii and L. Shaikhet, Stability of epidemic model with time delays influenced by stochastic perturbations, Mathematics and Computers in Simulation (Special Issue "Delay Systems"), 45 (1998), 269-277.
doi: 10.1016/S0378-4754(97)00106-7. |
| [3] |
N. Bradul and L. Shaikhet, Stability of the positive point of equilibrium of Nicholson's blowflies equation with stochastic perturbations: Numerical analysis, Discrete Dynamics in Nature and Society, 2007 (2007), 25 pp.
doi: 10.1155/2007/92959. |
| [4] |
M. Carletti, On the stability properties of a stochastic model for phage-bacteria interaction in open marine environment, Mathematical Biosciences, 175 (2002), 117-131.
doi: 10.1016/S0025-5564(01)00089-X. |
| [5] |
I. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations, Springer-Verlag, Berlin, 1972. |
| [6] |
M. Jovanovic and M. Krstic, Stochastically perturbed vector-borne disease models with direct transmission, Applied Mathematical Modelling, 36 (2012), 5214-5228.
doi: 10.1016/j.apm.2011.11.087. |
| [7] |
B. Mukhopadhyay and R. Bhattacharyya, A nonlinear mathematical model of virus-tumor-immune system interaction: Deterministic and stochastic analysis, Stochastic Analysis and Applications, 27 (2009), 409-429.
doi: 10.1080/07362990802679067. |
| [8] |
R. R. Sarkar and S. Banerjee, Cancer self remission and tumor stability - a stochastic approach, Mathematical Biosciences, 196 (2005), 65-81.
doi: 10.1016/j.mbs.2005.04.001. |
| [9] |
L. Shaikhet, Lyapunov Functionals and Stability of Stochastic Difference Equations, Springer, London, Dordrecht, Heidelberg, New York, 2011.
doi: 10.1007/978-0-85729-685-6. |
| [10] |
L. Shaikhet, Lyapunov Functionals and Stability of Stochastic Functional Differential Equations, Springer, Dordrecht, Heidelberg, New York, London, 2013.
doi: 10.1007/978-3-319-00101-2. |
| [11] |
J. Yoon, V. Hrynkiv, L. Morano A. Nguyen, S. Wilder and F. Mitchell, Mathematical modeling of Glassy-winged sharpshooter population, Mathematical Biosciences and Engineering, 11 (2014), 667-677.
doi: 10.3934/mbe.2014.11.667. |
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