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Stability of a positive equilibrium state for a stochastically perturbed mathematical model of glassywinged sharpshooter population
1.  Department of Higher Mathematics, Donetsk State University of Management, Chelyuskintsev str., 163a, Donetsk, 83015 
References:
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M. Bandyopadhyay and J. Chattopadhyay, Ratio dependent predatorprey model: Effect of environmental fluctuation and stability, Nonlinearity, 18 (2005), 913936. doi: 10.1088/09517715/18/2/022. 
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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), 269277. doi: 10.1016/S03784754(97)001067. 
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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 phagebacteria interaction in open marine environment, Mathematical Biosciences, 175 (2002), 117131. doi: 10.1016/S00255564(01)00089X. 
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I. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations, SpringerVerlag, Berlin, 1972. 
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M. Jovanovic and M. Krstic, Stochastically perturbed vectorborne disease models with direct transmission, Applied Mathematical Modelling, 36 (2012), 52145228. doi: 10.1016/j.apm.2011.11.087. 
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B. Mukhopadhyay and R. Bhattacharyya, A nonlinear mathematical model of virustumorimmune system interaction: Deterministic and stochastic analysis, Stochastic Analysis and Applications, 27 (2009), 409429. 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), 6581. 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: 10.1007/9780857296856. 
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L. Shaikhet, Lyapunov Functionals and Stability of Stochastic Functional Differential Equations, Springer, Dordrecht, Heidelberg, New York, London, 2013. doi: 10.1007/9783319001012. 
[11] 
J. Yoon, V. Hrynkiv, L. Morano A. Nguyen, S. Wilder and F. Mitchell, Mathematical modeling of Glassywinged sharpshooter population, Mathematical Biosciences and Engineering, 11 (2014), 667677. doi: 10.3934/mbe.2014.11.667. 
show all references
References:
[1] 
M. Bandyopadhyay and J. Chattopadhyay, Ratio dependent predatorprey model: Effect of environmental fluctuation and stability, Nonlinearity, 18 (2005), 913936. doi: 10.1088/09517715/18/2/022. 
[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), 269277. doi: 10.1016/S03784754(97)001067. 
[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 phagebacteria interaction in open marine environment, Mathematical Biosciences, 175 (2002), 117131. doi: 10.1016/S00255564(01)00089X. 
[5] 
I. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations, SpringerVerlag, Berlin, 1972. 
[6] 
M. Jovanovic and M. Krstic, Stochastically perturbed vectorborne disease models with direct transmission, Applied Mathematical Modelling, 36 (2012), 52145228. doi: 10.1016/j.apm.2011.11.087. 
[7] 
B. Mukhopadhyay and R. Bhattacharyya, A nonlinear mathematical model of virustumorimmune system interaction: Deterministic and stochastic analysis, Stochastic Analysis and Applications, 27 (2009), 409429. doi: 10.1080/07362990802679067. 
[8] 
R. R. Sarkar and S. Banerjee, Cancer self remission and tumor stability  a stochastic approach, Mathematical Biosciences, 196 (2005), 6581. 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: 10.1007/9780857296856. 
[10] 
L. Shaikhet, Lyapunov Functionals and Stability of Stochastic Functional Differential Equations, Springer, Dordrecht, Heidelberg, New York, London, 2013. doi: 10.1007/9783319001012. 
[11] 
J. Yoon, V. Hrynkiv, L. Morano A. Nguyen, S. Wilder and F. Mitchell, Mathematical modeling of Glassywinged sharpshooter population, Mathematical Biosciences and Engineering, 11 (2014), 667677. doi: 10.3934/mbe.2014.11.667. 
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