Citation: Sanling Yuan, Xuehui Ji, Huaiping Zhu. Asymptotic behavior of a delayed stochastic logistic model with impulsive perturbations[J]. Mathematical Biosciences and Engineering, 2017, 14(5&6): 1477-1498. doi: 10.3934/mbe.2017077
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[1] | [ S. Aida,S. Kusuoka,D. Strook, On the support of Wiener functionals, Longman Scient. Tech., 284 (1993): 3-34. |
[2] | [ T. Alkurdi,S. Hille,O. Gaans, Ergodicity and stability of a dynamical system perturbed by impulsive random interventions, J. Math. Anal. Appl., 407 (2013): 480-494. |
[3] | [ L. Arnold, Stochastic Differential Equations: Theory and Applications, Wiley, New York-London-Sydney, 1974. |
[4] | [ I. Barbalat, Systems dequations differentielles d'osci d'oscillations nonlineaires, Rev. Roumaine Math. Pures Appl., 4 (1959): 267-270. |
[5] | [ G. Ben Arous,R. Léandre, Décroissance exponentielle du noyau de la chaleur sur la diagonale (Ⅱ), Probab. Theory Related Fields, 90 (1991): 377-402. |
[6] | [ A. Freedman, Stochastic differential equations and their applications, Stochastic Differential Equations, 77 (1976): 75-148. |
[7] | [ S. Foguel, Harris operators, Israel J. Math., 33 (1979): 281-309. |
[8] | [ K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, Springer-Verlag, New York, 1992. |
[9] | [ R. Z. Has'minskii, Stochastic Stability of Differential Equations, Sijthoof & Noordhoof, Alphen aan den Rijn, The Netherlands, 1980. |
[10] | [ D. Higham, An algorithmic introduction to numerical simulation of stochastic differential equations, SIAM Review, 43 (2001): 525-546. |
[11] | [ D. Jiang,N. Shi, A note on nonautonomous logistic equation with random perturbation, J. Math. Anal. Appl., 303 (2005): 164-172. |
[12] | [ D. Jiang,N. Shi,X. Li, Global stability and stochastic permanence of a non-autonomous logistic equation with random perturbation, J. Math. Anal. Appl., 340 (2008): 588-597. |
[13] | [ I. Karatzas and S. Shreve, Brownian Motion and Stochastic Calculus, Springer Verlag, Berlin, 1991. |
[14] | [ Y. Kuang, Delay differential equations with applications in population dynamics, in Mathematics in Science and Engineering, Academic Press, New York, 1993. |
[15] | [ X. Li,X. Mao, Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation, Discrete Contin. Dyn. Syst., 24 (2009): 523-545. |
[16] | [ M. Liu,K. Wang, Persistence and extinction in stochastic non-autonomous logistic systems, J. Math. Anal. Appl., 375 (2011): 443-457. |
[17] | [ M. Liu,K. Wang, On a stochastic logistic equation with impulsive perturbations, Comput. Math. Appl., 63 (2012): 871-886. |
[18] | [ Z. Ma and Y. Zhou, Qualitative and Stability Method of Ordinary Differential Equation, Science Press, Beijing, 2001. |
[19] | [ M. Mackey,M. Kamińska,R. Yvinec, Molecular distributions in gene regulatory dynamics, J. Theoret. Biol., 247 (2011): 84-96. |
[20] | [ X. Mao, Stochastic Differential Equations and their Applications, Horwood publishing, Chichester, England, 1997. |
[21] | [ J. Norris, Simplified Malliavin calculus, in SLeminaire de probabilitiLes XX, Lecture Notes in Mathematics, Springer, New York, 1024 (1986), 101–130. |
[22] | [ K. Pichór,R. Rudnicki, Stability of Markov semigroups and applications to parabolic systems, J. Math. Anal. Appl., 215 (1997): 56-74. |
[23] | [ K. Pichór,R. Rudnicki, Continuous Markov semigroups and stability of transport equations, J. Math. Anal. Appl., 249 (2000): 668-685. |
[24] | [ S. Ruan, Delay differential equations in single species dynamics, in Delay Differential Equations and Applications, Springer, Berlin, 205 (2006), 477–517. |
[25] | [ R. Rudnicki, On asymptotic stability and sweeping for Markov operators, Bull. Polish Acad. Math., 43 (1995): 245-262. |
[26] | [ J. Yan, On the oscillation of impulsive neutral delay differential equations, Chinese Ann. Math., 21A (2000): 755-762. |
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