`a`
Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

Models of the population playing the rock-paper-scissors game
Pages: 1 - 11, Issue 1, January 2018

doi:10.3934/dcdsb.2018001      Abstract        References        Full text (449.2K)           Related Articles

Włodzimierz Bąk - Instytut Matematyki i Informatyki, Uniwersytet Opolski, ul. Oleska 48, Poland (email)
Tadeusz Nadzieja - Instytut Matematyki i Informatyki, Uniwersytet Opolski, ul. Oleska 48, Poland (email)
Mateusz Wróbel - Instytut Matematyki i Informatyki, Uniwersytet Opolski, ul. Oleska 48, Poland (email)

1 K. Barański and M. Misiurewicz, Omega-limit set for the Stein-Ulam spiral map, Topology Proceedings, 36 (2010), 145-172.       
2 A. Gaunersdorfer, Time averages for heteroclinic attractors, SIAM J. Math. Anal., 52 (1992), 1476-1489.       
3 J. Guckenheimer, Bifurcations of dynamical systems, C.I.M.E Summer School Bressanone 1978, Progr. Math., Birkhäuser, Boston, Mass., 8 (1980), 115-231.       
4 G. N. Hardy, Mendelian proportions in a mixed population, Science, 28 (1908), 49-50.
5 J. Hofbauer and K. Sigmund, Evolutionary Games and Population Dynamics, Cambridge University Press, Cambridge, 1998.       
6 Yu I. Lyubich, Basic concepts and theorem of the evolutionary genetics of free populations, Russian Math. Surveys, 26 (1971), 51-116.       
7 M. T. Menzel, P. R. Stein and S. M. Ulam, Quadratic Transformations. Part 1, in Los Alamos Scientific Laboratory report LA-2305, 1959.
8 F. Takens, Heteroclinic attractors: Time averages and moduli of topological conjugacy, Bol. Soc. Bras. Mat., 25 (1994), 107-120.       
9 F. Takens, Orbits with historic behaviour, or non-existence of averages, Nonlinearity, 21 (2008), T33-T36.       
10 S. M. Ulam, A Collection of Mathematical Problems, Interscience Tracts in Pure and Applied Mathematics, no. 8, New York-London, Interscience Publishers, 1960.       
11 S. S. Vallander, The limiting behavior of the sequence of iterates of certain quadratic transformations, (Russian)Dokl. Akad. Nauk SSSR, 202 (1972), 515-517.       
12 W. Weinberg, Über den Nachweis der Vererbung beim Menschen, Jahreshefte Verein f. Vaterl. Naturk., in Würtembergh, 64 (1908), 368-383.
13 D. Whitley, Discrete dynamical systems in dimensions one and two, Bull. London Math. Soc., 15 (1983), 177-217.       
14 M. I. Zaharevič, On the behavior of trajectories and the ergodic hypothesis for quadratic mappings of a simplex, Russian Math. Surveys, 33 (1978), 265-266.       

Go to top