Stability of the positive point of equilibrium of Nicholson's blowflies equation with stochastic perturbations: Numerical analysis

Discrete Dynamics in Nature and Society

Volumn 2007, Issue 1, 2007, Pages

  Bradul, Nataliya ^a   Shaikhet, Leonid ^a  

^a Mariupol State University   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

CALLIPHORIDAE;

EID: 34548739542     PISSN: 10260226     EISSN: 1607887X     Source Type: Journal    
DOI: 10.1155/2007/92959     Document Type: Article

References (34)

1. X. Ding W. Li Stability and bifurcation of numerical discretization Nicholson blowflies equation with delay Discrete Dynamics in Nature and Society 2006 2006 19413 12 pages
2. Q. X. Feng J. R. Yan Global attractivity and oscillation in a kind of Nicholson's blowflies Journal of Biomathematics 17 2002 1 21-26
3. W. S. Gurney S. P. Blytne R. M. Nisbet Nicholson's blowflies revisited Nature 287 1980 17-21
4. V. Lj. Kocić G. Ladas Oscillation and global attractivity in a discrete model of Nicholson's blowflies Applicable Analysis 38 1990 1-2 21-31
5. M. R. S. Kulenović G. Ladas Y. G. Sficas Global attractivity in Nicholson's blowflies Applicable Analysis 43 1992 1-2 109-124
6. J. Li Global attractivity in Nicholson's blowflies Applied Mathematics. Series B 11 1996 4 425-434
7. J Li Global attractivity in a discrete model of Nicholson's blowflies Annals of Differential Equations 12 1996 2 173-182
8. M. Li J. Yan Oscillation and global attractivity of generalized Nicholson's blowfly model Differential Equations and Computational Simulations (Chengdu, 1999) 196-201 World Scientific River Edge, NJ, USA 2000
9. J. W.-H. So J. S. Yu Global attractivity and uniform persistence in Nicholson's blowflies Differential Equations and Dynamical Systems 2 1994 1 11-18
10. J. W.-H. So J. S. Yu On the stability and uniform persistence of a discrete model of Nicholson's blowflies Journal of Mathematical Analysis and Applications 193 1995 1 233-244
11. J. Wei M. Y. Li Hopf bifurcation analysis in a delayed Nicholson blowflies equation Nonlinear Analysis 60 2005 7 1351-1367
12. I. Györi G. Ladas Oscillation Theory of Delay Differential Equations: With Applications Oxford Mathematical Monographs The Clarendon Press, Oxford University Press New York, NY, USA 1991 xii+368
13. M. R. S. Kulenović G. Ladas Linearized oscillations in population dynamics Bulletin of Mathematical Biology 49 1987 5 615-627
14. M. R. S. Kulenović G. Ladas Y. G. Sficas Global attractivity in population dynamics Computers & Mathematics with Applications 18 1989 10-11 925-928
15. E. Beretta V. Kolmanovskiǐ L. Shaikhet Stability of epidemic model with time delays influenced by stochastic perturbations Mathematics and Computers in Simulation 45 1998 3-4 269-277
16. B. Paternoster L. Shaikhet About stability of nonlinear stochastic difference equations Applied Mathematics Letters 13 2000 5 27-32
17. L. Shaikhet Stability in probability of nonlinear stochastic systems with delay Matematicheskie Zametki 57 1995 1 Russian 142-146 translation in Mathematical Notes, vol. 57, no. 1, pp. 103-106, 1995
18. L. Shaikhet Stability in probability of nonlinear stochastic hereditary systems Dynamic Systems and Applications 4 1995 2 199-204
19. L. Shaikhet Stability of predator-prey model with aftereffect by stochastic perturbation Stability and Control: Theory and Applications 1 1998 1 3-13
20. V. B. Kolmanovskiǐ L. Shaikhet New results in stability theory for stochastic functional-differential equations (SFDEs) and their applications Proceedings of Dynamic Systems and Applications 1 Dynamic Atlanta, Ga, USA 1994 167-171
21. V. B. Kolmanovskiǐ L. Shaikhet A method for constructing Lyapunov functionals for stochastic differential equations of neutral type Differentsialniye Uravneniya Russian 31 1995 11 1851-1857 translation in Differential Equations, vol. 31, no. 11, pp. 1819-1825, 1995
22. V. B. Kolmanovskiǐ L. Shaikhet General method of Lyapunov functionals construction for stability investigation of stochastic difference equations Dynamical Systems and Applications World Sci. Ser. Appl. Anal. 4 1995 World Scientific River Edge, NJ, USA 397-439
23. V. Kolmanovskiǐ L. Shaikhet Some peculiarities of the general method of Lyapunov functionals construction Applied Mathematics Letters 15 2002 3 355-360
24. V. Kolmanovskiǐ L. Shaikhet Construction of Lyapunov functionals for stochastic hereditary systems: A survey of some recent results Mathematical and Computer Modelling 36 2002 6 691-716
25. V. Kolmanovskiǐ L. Shaikhet About one application of the general method of Lyapunov functionals construction International Journal of Robust and Nonlinear Control 13 2003 9 805-818
26. L. Shaikhet Modern state and development perspectives of Lyapunov functionals method in the stability theory of stochastic hereditary systems Theory of Stochastic Processes 2(18) 1996 1-2 248-259
27. Ǐ. I. Gikhman A. V. Skorokhod The Theory of Stochastic Processes I Die Grundlehren der mathematischen Wissenschaften 210 Springer Berlin, Germany 1974 viii+570
28. Ǐ. I. Gikhman A. V. Skorokhod The Theory of Stochastic Processes II Grundlehren der mathematischen Wissenschaften 218 Springer Berlin, Germany 1975 VII+441
29. Ǐ. I. Gikhman A. V. Skorokhod The Theory of Stochastic Processes III Grundlehren der mathematischen Wissenschaften 232 Springer Berlin, Germany 1979 iii+387
30. V. B. Kolmanovskiǐ V. R. Nosov Stability of Functional-Differential Equations Mathematics in Science and Engineering 180 Academic Press London, UK 1986 xiv+217
31. L. Shaikhet Necessary and sufficient conditions of asymptotic mean square stability for stochastic linear difference equations Applied Mathematics Letters 10 1997 3 111-115
32. M. Bandyopadhyay J. Chattopadhyay Ratio-dependent predator-prey model: effect of environmental fluctuation and stability Nonlinearity 18 2005 2 913-936
33. M. Carletti On the stability properties of a stochastic model for phage-bacteria interaction in open marine environment Mathematical Biosciences 175 2002 2 117-131
34. S. I. Resnick Adventures in Stochastic Processes Birkhäuser Boston, Mass, USA 1992 xii+626