http://orcid.org/0000-0002-1054-4568
References
- L. Arnold, Stochastic Differential Equations: Theory and Applications, Wiley Interscience, New York, 1974.
- P. Auger, R.B. de La Parra, J.-C. Poggiale, E. Sánchez, and L. Sanz, Aggregation methods in dynamical systems and applications in population and community dynamics, Phys. Life Rev. 5(2) (2008), pp. 79–105. doi: 10.1016/j.plrev.2008.02.001
- P. Auger, J. Poggiale, and E. Sánchez, A review on spatial aggregation methods involving several time scales, Ecol. Complex. 10 (2012), pp. 12–25. doi: 10.1016/j.ecocom.2011.09.001
- H. Baumgärtel, Analytic Perturbation Theory for Matrices and Operators, Vol. 15, Springer, New York, 1985.
- N. Berglund and B. Gentz, Geometric singular perturbation theory for stochastic differential equations, J. Differential Equations 191(1) (2003), pp. 1–54. doi: 10.1016/S0022-0396(03)00020-2
- C.A. Braumann, Variable effort fishing models in random environments, Math. Biosci. 156(1) (1999), pp. 1–19. doi: 10.1016/S0025-5564(98)10058-5
- C.A. Braumann, Harvesting in a random environment: Itô or stratonovich calculus? J. Theoret. Biol. 244(3) (2007), pp. 424–432. doi: 10.1016/j.jtbi.2006.08.029
- C. Carlos and C.A. Braumann, General population growth models with allee effects in a random environment, Ecol. Complex. 30 (2016), pp. 26–33. doi: 10.1016/j.ecocom.2016.09.003
- M. Fiedler, Special Matrices and their Applications in Numerical Mathematics, Kluwer Boston, Inc., 1986.
- N. Herath and D. Del Vecchio, Model order reduction for linear noise approximation using time-scale separation, in 2016 IEEE 55th Conference on Decision and Control (CDC), IEEE, Chicago, IL, USA, 2016, pp. 5875–5880.
- N. Herath and D. Del Vecchio, Model reduction for a class of singularly perturbed stochastic differential equations: Fast variable approximation, in American Control Conference (ACC), 2016, IEEE, Boston, MA, USA, 2016, pp. 3674–3679.
- R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 2012.
- D. Jiang, J. Yu, C. Ji, and N. Shi, Asymptotic behavior of global positive solution to a stochastic sir model, Math. Comput. Modelling 54(1) (2011), pp. 221–232. doi: 10.1016/j.mcm.2011.02.004
- Y. Kabanov and S. Pergamenshchikov, Two-Scale Stochastic Systems: Asymptotic Analysis and Control, Vol. 49, Springer, Berlin, 2003.
- R. Khasminskii, Stochastic Stability of Differential Equations, Vol. 66, Springer, Berlin, 2012.
- H.J. Kushner, Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems, Vol. 3, Birkhäuser, Boston, 1990.
- J.A. Linda, An Introduction to Mathematical Biology, Pearson, Upper Saddle River, NJ, 2007.
- X. Mao, Stochastic Differential Equations and their Applications, Woodhead Publishing; 2nd ed. ( January 13, 2008), Oxford, 1997.
- L. Sanz and J. Alonso, Approximate aggregation methods in discrete time stochastic population models, Math. Model. Nat. Pheno. 5(6) (2010), pp. 38–69. doi: 10.1051/mmnp/20105603
- L. Sanz and R. Bravo de la Parra, Variables aggregation in a time discrete linear model, Math. Biosci. 157(1) (1999), pp. 111–146. doi: 10.1016/S0025-5564(98)10079-2
- L. Sanz, A. Blasco, and R. Bravo de la Parra, Approximate reduction of multi-type Galton–Watson processes with two time scales, Math. Models Methods Appl. Sci. 13(04) (2003), pp. 491–525. doi: 10.1142/S0218202503002659
- E. Seneta, Non-Negative Matrices and Markov Chains, Springer Science & Business Media, New York, 2006.
- M. Turelli, Random environments and stochastic calculus, Theoret. Popul. Biol. 12(2) (1977), pp. 140–178. doi: 10.1016/0040-5809(77)90040-5
- C. Xu and S. Yuan, Competition in the chemostat: A stochastic multi-species model and its asymptotic behavior, Math. Biosci. 280 (2016), pp. 1–9. doi: 10.1016/j.mbs.2016.07.008