Free Access
Math. Model. Nat. Phenom.
Volume 9, Number 3, 2014
Biological evolution
Page(s) 47 - 67
Published online 28 May 2014
  1. G. I. Barenblatt, V. M. Entov, V. M. Ryzhik. Theory of fluid flows through natural rocks. Kluwer Academic Publishers, 1989. [Google Scholar]
  2. A. S. Bratus, C.-K. Hu, M. V. Safro, A. S. Novozhilov. On diffusive stability of Eigen’s quasispecies model. Journal of Dynamical and Control Systems. arXiv:1212.1488 (2013). [Google Scholar]
  3. A. S. Bratus, A. S. Novozhilov, A. P. Platonov. Dynamical systems and models in biology. Fizmatlit, 2010. in Russian. [Google Scholar]
  4. A. S. Bratus, V. P. Posvyanskii. Stationary solutions in a closed distributed Eigen–Schuster evolution system. Diff. Eq., 42 (2006), 1762–1774. [CrossRef] [Google Scholar]
  5. A. S. Bratus, V. P. Posvyanskii, A. S. Novozhilov. Existence and stability of stationary solutions to spatially extended autocatalytic and hypercyclic systems under global regulation and with nonlinear growth rates. Nonl. Anal. Real World Appl., 11 (2010), 1897–1917. [CrossRef] [Google Scholar]
  6. A. S. Bratus, V. P. Posvyanskii, A. S. Novozhilov. A note on the replicator equation with explicit space and global regulation. Math. Bios. Eng., 8 (2011), 659–676. [Google Scholar]
  7. R. S. Cantrell, C. Cosner. Spatial ecology via reaction-diffusion equations. Wiley, 2003. [Google Scholar]
  8. R. Cressman, A. T. Dash. Density dependence and evolutionary stable strategies. J. Theor. Biol., 126 (1987), 393–406. [CrossRef] [Google Scholar]
  9. R. Cressman, G. T. Vickers. Spatial and Density Effects in Evolutionary Game Theory. J. Theor. Biol., 184 (1997), 359–369. [CrossRef] [PubMed] [Google Scholar]
  10. U. Dieckmann, R. Law, J. A. J. Metz. The Geometry of Ecological Interactions: Simplifying Spatial Complexity. Cambridge University Press, 2000. [Google Scholar]
  11. M. Eigen, J. McCascill, P. Schuster. The Molecular Quasi-Species. Adv. Chem. Phys., 75 (1989), 149–263. [Google Scholar]
  12. L. C. Evans. Partial Differential Equations. American Mathematical Society, 2nd edition, 2010. [Google Scholar]
  13. R. Ferriere, R. E. Michod. Wave patterns in spatial games and the evolution of cooperation. In U. Dieckmann, R. Law, and J. A. J. Metz, editors, The Geometry of Ecological Interactions: Simplifying Spatial Complexity, Cambridge University Press, (2000), 318–339. [Google Scholar]
  14. K. P. Hadeler. Diffusion in Fisher’s population model. R. Moun. J. Math., 11 (1981), 39–45. [CrossRef] [MathSciNet] [Google Scholar]
  15. J. Hofbauer, K. Sigmund. Evolutionary Games and Population Dynamics. Cambridge University Press, 1998. [Google Scholar]
  16. J. Hofbauer, K. Sigmund. Evolutionary game dynamics. Bull. Am. Math. Soc., 40 (2003), 479–519. [CrossRef] [Google Scholar]
  17. V. C. L. Hutson, G. T. Vickers. Travelling waves and dominance of ESS’s. J. Math. Biol., 30 (1992), 457–471. [CrossRef] [MathSciNet] [Google Scholar]
  18. V. C. L. Hutson, G. T. Vickers. The Spatial Struggle of Tit-For-Tat and Defect. Phil. Trans. Royal Soc. Ser. B: Biol. Sc., 348 (1995), 393–404. [Google Scholar]
  19. G. P. Karev, A. S. Novozhilov, F. S. Berezovskaya. On the asymptotic behavior of the solutions to the replicator equation. Math. Med. Biol., 28 (2011), 89–110. [Google Scholar]
  20. P. Knabner, L. Angerman. Numerical methods for elliptic and parabolic partial differential equations, vol. 44. Springer, 2003. [Google Scholar]
  21. S. G. Mikhlin. Variational Methods in Mathematical Physics. Pergamon Press, 1964. [Google Scholar]
  22. A. S. Novozhilov, V. P. Posvyanskii, A. S. Bratus. On the reaction–diffusion replicator systems: spatial patterns and asymptotic behaviour. Russ. J. Num. Anal. Math. Mod., 26 (2012), 555–564. [Google Scholar]
  23. M. A. Nowak. Evolutionary dynamics: exploring the equations of life. Harvard University Press, 2006. [Google Scholar]
  24. K. Rektorys. Variational methods in mathematics, science and engineering. Springer, 1980. [Google Scholar]
  25. N. Vaidya, M. L. Manapat, I. A. Chen, R. Xulvi-Brunet, E. J. Hayden, N. Lehman. Spontaneous network formation among cooperative rna replicators. Nature, 491 (2012), 72–77. [CrossRef] [PubMed] [Google Scholar]
  26. G. T. Vickers. Spatial patterns and ESS’s. J. Theor. Biol., 140 (1989), 129–35. [CrossRef] [PubMed] [Google Scholar]
  27. G. T. Vickers. Spatial patterns and travelling waves in population genetics. J. Theor. Biol., 150 (1991), 329–337. [CrossRef] [PubMed] [Google Scholar]
  28. G. T. Vickers, V. C. L. Hutson, C. J. Budd. Spatial patterns in population conflicts. J. Math. Biol., 31 (1993), 411–430. [CrossRef] [MathSciNet] [Google Scholar]
  29. E. D. Weinberger. Spatial stability analysis of Eigen’s quasispecies model and the less than five membered hypercycle under global population regulation. Bull. Math. Biol., 53 (1991), 623–638. [CrossRef] [Google Scholar]

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