Normal Forms and Unfoldings of Singular Strategy Functions

详细信息    查看全文

• 作者：Amit Vutha ; Martin Golubitsky
• 关键词：singularity theory ; Adaptive dynamics ; Hawk ; dove game
• 刊名：Dynamic Games and Applications
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：5
• 期：2
• 页码：180-213
• 全文大小：1,332 KB
• 参考文献：1.Champagnat N, Ferriere R, Arous GB (2001) The canonical equation of adaptive dynamics: a mathematical view. Selection 2:73-3View Article
  2.Damon J (1984) The unfolding and determinacy theorems for subgroups \(A\) and \(K\) . Mem Am Math Soc 50:306MathSciNet
  3.Dieckmann U, Doebeli M, Metz JAJ (2004) Adaptive speciation. In: Tautz D (ed) Cambridge studies in adaptive dynamics. Cambridge University Press, Cambridge
  4.Dieckmann U, Law R (1996) The dynamical theory of coevolution: a derivation from stochastic ecological processes. J Math Biol 34:569-12View Article MathSciNet
  5.Dieckmann U, Metz JAJ (2006) Surprising evolutionary predictions from enhanced ecological realism. Theor Popul Biol 69:263-81View Article MATH
  6.Dercole F, Rinaldi S (2008) Analysis of evolutionary processes: the adaptive dynamics approach and its applications. Princeton Series in Theoretical and Computational Biology, Princeton University Press, PrincetonView Article
  7.Eshel I, Motro U, Sansone E (1997) Continuous stability and evolutionary convergence. J Theor Biol 185:333-43View Article
  8.Geritz SAH, Metz JAJ, Kisdi é, Meszéna G (1997) Dynamics of adaptation and evolutionary branching. Phys Rev Lett 78:2024-027View Article
  9.Geritz SAH, van der Meijden E, Metz JAJ (1999) Evolutionary dynamics of seed size and seedling competitive ability. Theor Popul Biol 55:324-43View Article MATH
  10.Golubitsky M (1978) An introduction to catastrophe theory and its applications. SIAM Rev 20(2):352-87View Article MATH MathSciNet
  11.Golubitsky M, Schaeffer DG (1984) Singularities and groups in bifurcation theory. Applied mathematics science, vol 1. Springer, New York
  12.Mather J (1968) Stability of mappings, III. Finitely determined map-germs. Publ Math 35:127-56View Article MATH
  13.Maynard-Smith J (1982) Evolution and theoory of games. Cambridge University Press, CambridgeView Article
  14.Maynard-Smith J, Price GR (1973) The logic of animal conflict. Nature 246:15-8View Article
  15.McGill B, Brown J (2007) Evolutionary game theory and adaptive dynamics of continuous traits. Annu Rev Ecol Evol Syst 38:403-35View Article
  16.Poston T, Stewart I (1978) Catastrophe theory and its applications. Pitman, San FranciscoMATH
  17.Thom R (1972) Structural stability and morphogenesis: an outline of a general theory of models. Benjamin, Reading
  18.Vincent TL, Brown JS (1988) The evolution of ESS theory. Annu Rev Ecol Syst 19:423-43View Article
  19.Vutha A (2013) Normal forms and unfoldings of singular strategy functions. Department of Mathematics, The Ohio State University, December, Thesis
  20.Waxman D, Gavrilets S (2005) 20 Questions on adaptive dynamics. J Evol Biol 18(5):1139-154View Article
  21.Zeeman EC (1977) Catastrophe theory: selected papers 1972-977. Addison-Wesley, LondonMATH
  
• 作者单位：Amit Vutha (1)
  Martin Golubitsky (2)
  
  1. Department of Mathematics, The Ohio State University, Columbus, OH, 43210, USA
  2. Mathematical Biosciences Institute, The Ohio State University, Columbus, OH?, 43210, USA
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Economics
  Communications Engineering and Networks
  Operations Research and Mathematical Programming
  Game Theory, Economics, Social and Behavioral Sciences
  Game Theory and Mathematical Methods
  
• 出版者：Birkh盲user Boston
• ISSN：2153-0793

文摘

We study adaptive dynamics strategy?functions by defining a form of equivalence that preserves key properties of these functions near singular points (such as whether or not a singularity is an evolutionary or a convergent stable strategy). Specifically, we compute and classify normal forms and low codimension universal unfoldings of these functions. These calculations lead to a classification of local pairwise invasibility plots that can be expected in systems with two parameters. This problem is complicated because the allowable coordinate changes at such points are restricted by the specific nature of strategy?functions; hence the needed singularity theory is not the standard one. We also show how to use the singularity theory results to help study a specific adaptive game: a generalized hawk—dove game studied previously by Dieckmann and Metz.