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Exponential stability of numerical solutions to a stochastic age-structured population system with diffusion. (English) Zbl 1149.65009
Author’s summary: The main aim of this paper is to investigate the exponential stability of the Euler method for a stochastic age-structured population system with diffusion. The definition of exponential mean-square stability of a numerical method is introduced. It is proved that the Euler scheme is exponentially stable in mean square sense. An example is given for illustration.
MSC:
65C30Stochastic differential and integral equations
60H35Computational methods for stochastic equations
65L06Multistep, Runge-Kutta, and extrapolation methods
65L20Stability and convergence of numerical methods for ODE
92D25Population dynamics (general)
60H10Stochastic ordinary differential equations
34F05ODE with randomness
References:
[1]Allen, L. J. S.; Thrasher, D. B.: The effects of vaccination in an age-dependent model for varicella and herpes zoster, IEEE trans. Automat. control 43, 779-789 (1998)
[2]Arnold, L.: Stochastic differential equations: theory and applications, (1972)
[3]Caraballo, T.; Real, J.: On the pathwise exponential stability of non-linear stochastic partial differential equations, Stochastic anal. Appl. 83, No. 5, 517-525 (1994) · Zbl 0808.93069 · doi:10.1080/07362999408809370
[4]Caraballo, T.; Liu, K.: On exponential stability criteria of stochastic partial differential equations, Stochastic process. Appl. 83, 289-301 (1999) · Zbl 0997.60065 · doi:10.1016/S0304-4149(99)00045-9
[5]Cushing, J. M.: The dynamics of hierarchical age-structured populations, J. math. Biol. 32, 705-729 (1994) · Zbl 0823.92018 · doi:10.1007/BF00163023
[6]Hernandez, E. Gaston: Age-density dependent population dispersal in RN, Math. biosci. 149, 37-56 (1998) · Zbl 0947.92026 · doi:10.1016/S0025-5564(97)10014-1
[7]Kloeden, P. E.; Platen, E.: Numerical solution of stochastic differential equations, (1992) · Zbl 0752.60043
[8]Mao, X.: Stochastic differential equations and applications, (1997)
[9]Marion, G.; Mao, X.; Renshaw, E.: Convergence of the Euler scheme for a class of stochastic differential equation, Internat. math. J. 1, No. 1, 9-22 (2002) · Zbl 0987.60068
[10]Platen, E.: An introduction to numerical methods for stochastic differential equations, Acta numerica 8, 197-246 (1999) · Zbl 0942.65004
[11]Pollard, J. H.: On the use of the direct matrix product in analyzing certain stochastic population model, Biometrika 53, 397-415 (1966) · Zbl 0144.43901
[12]Fister, K. Renee; Lenhart, S.: Optimal control of a competitive system with age-structure, J. math. Anal. appl. 291, 526-537 (2004) · Zbl 1043.92031 · doi:10.1016/j.jmaa.2003.11.031
[13]Ronghua, L.; Hongbing, M.; Qin, C.: Exponential stability of numerical solutions to sddes with Markovian switching, Appl. math. Comput. 174, No. 2, 1302-1313 (2006) · Zbl 1105.65010 · doi:10.1016/j.amc.2005.05.037
[14]Zhang, Q. -M.; Wen-An, L.; Zan-Kan, N.: Existence, uniqueness and exponential stability for stochastic age-dependent population, Appl. math. Comput. 154, 183-201 (2004) · Zbl 1051.92033 · doi:10.1016/S0096-3003(03)00702-1
[15]Zhang, Q. M.; Zhao, H. Chong: Numerical analysis for stochastic age-dependent population equations, Appl. math. Comput. 176, 210-223 (2005)