References
- A.S.Ackleh, Y.Dib, and S.Jang, A discrete-time Beverton–Holt competition model, in Difference Equations and Discrete Dynamical Systems, L.J.S.Allen, B.Aulback, S.Elaydi, and R.Sacker, eds., World Scientific, New Jersey, 2005, pp. 1–10.
- A.S.Ackleh, B.G.Fitzpatrick, and H.R.Thieme, Rate distributions and survival of the fittest: a formulation on the space of measures, Discrete Contin. Dyn. Syst. Ser. B5 (2005), pp. 917–928.
- A.S.Ackleh and S.Hu, Comparison between stochastic and deterministic selection–mutation models, Math. Biosci. Eng.4 (2007), pp. 133–157.
- A.S.Ackleh, D.F.Marshall, H.E.Heatherly, and B.G.Fitzpatrick, Survival of the fittest in a generalized logistic model, Math. Models Methods Appl. Sci.9 (1999), pp. 1379–1391.
- A.S.Ackleh, D.F.Marshall, and H.E.Heatherly, Extinction in a generalized Lotka-Volterra predator–prey model, J. Appl. Math. Stoch. Anal13 (2000), pp. 287–297.
- A.S.Ackleh and P.L.Salceanu, Robust uniform persistence and competitive exclusion in a non autonomous multi-strain SIR epidemic model with disease-induced mortality, J. Math. Biol. (2013). 10.1007/s00285-012-0636-4.
- L.J.S.Allen, N.Kirupaharan, and S.M.Wilson, SIS epidemic models with multiple pathogen strains, J. Differ. Eq. Appl.10 (2004), pp. 53–75.
- R.Bürger, Mutation–selection models in population genetics and evolutionary game theory, Acta Appl. Math.14 (1989), pp. 5–89.
- A.Calsina and S.Cuadrado, Small mutation rate and evolutionarily stable strategies in infinite dimensional adaptive dynamics, J. Math. Biol.48 (2004), pp. 135–159.
- A.Calsina and S.Cuadrado, Asymptotic stability of equilibria of selection–mutation equations, J. Math. Biol.54 (2007), pp. 489–511.
- Y.Chow and J.Hsieh, On multi-dimensional discrete-time Beverton–Holt competition models, J. Differ. Eq. Appl.19 (2013), pp. 491–506.
- J.Cleveland and A.S.Ackleh, Evolutionary game theory on measure spaces: Well-possedness, Nonlinear Anal. Real World Appl.14 (2013), pp. 785–797.
- R.Cressman and J.Hofbauer, Comparison between stochastic and deterministic selection–mutation models, Theor. Popul. Biol.67 (2005), pp. 47–59.
- L.Desvillettes, P.-E.Jabin, S.Mischler, and G.Raoul, On selection dynamics for continuous structured populations, Commun. Math. Sci.6(3) (2008), pp. 729–747.
- R.E.Mickens, Applications of Non-standard Finite Difference Schemes, World Scientific, New Jersey, 2000.
- K.Mischaikow, H.L.Smith, and H.R.Thieme, Asymptotically autonomous semiflows: Chain recurrence and Lyapunov functions, Trans. Am. Math. Soc.347 (1995), pp. 1669–1685.
- M.A.Nowak, Evolutionary Dynamics: Exploring the Equations of Life, Harvard University Press, Cambridge, MA, 2006.
- B.Perthame, Transport Equation in Biology, Frontiers in Mathematics Series, Birkhauser, Boston, 2005.
- G.Raoul, Local stability of evolutionary attractors for continuous structured populations, Monatsh. fur Math.165 (2012), pp. 117–144.
- G.Raoul, Long time evolution of populations under selection and vanishing mutations, Acta Appl. Math.114 (2011), pp. 1–14.
- P.L.Salceanu, Robust uniform persistence in discrete and continuous dynamical systems using Lyapunov exponents, Math. Biosci. Eng.8(3) (2011), pp. 807–825.
- P.L.Salceanu and H.L.Smith, Lyapunov exponents and persistence in discrete dynamical systems, Discrete Cont. Dyn-B12(1) (2009), pp. 187–203.
- H.L.Smith and H.Thieme, Dynamical Systems and Population Persistence, Graduate Stud. Math.118. American Mathematical Society, Providence, RI, 2011.
- H.L.Smith and P.Waltman, The Theory of the Chemostat, Cambridge University Press, Cambridge, 1995.
- H.L.Smith and P.Waltman, Perturbation of a globally stable steady state, Proc. AMS127(2) (1999), pp. 447–453.
- H.R.Thieme, Mathematics in Population Biology, Princeton University Press, Springer, Princeton, NJ, 2003.
- X-Q.Zhao, Dynamical Systems in Population Biology, Springer, New York, 2003.