Abstract
Biological as well as socio-economic populations can exhibit oscillatory dynamics. In the simplest case this can be described by oscillations around a neutral fixed point as in the classical Lotka-Volterra system. In reality, populations are always finite, which can be discussed in a general framework of a finite-size expansion which allows to derive stochastic differential equations of Fokker-Planck type as macroscopic evolutionary dynamics. Important applications of this concept are economic cycles for “cooperate—defect—tit for tat” strategies, mating behavior of lizards, and bacterial population dynamics which can all be described by cyclic games of rock-scissors-paper dynamics. Here one can study explicitly how the stability of coexistence is controlled by payoffs, the specific behavioral model and the population size. Finally, in socio-economic systems one is often interested in the stabilization of coexistence solutions to sustain diversity in an ecosystem or society. Utilizing a diversity measure as dynamical observable, a feedback into the payoff matrix is discussed which stabilizes the steady state of coexistence.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
J. von Neumann, O. Morgenstern, Theory of Games and Economic Behavior, (Princeton, 1944)
J. Nash, Proc. Natl. Acad. Sci. 36, 4849 (1950)
J.M. Smith, G.R. Price, Nature 246, 15–18 (1973)
J. Hofbauer, K. Sigmund, Evolutionary Games and Population Dynamics (Cambridge University Press, Cambridge, England, 1998)
M.A. Nowak, A. Sasaki, C. Taylor, D. Fudenberg, Nature 428, 646 (2004)
C. Taylor, D. Fudenberg, A. Sasaki, M.A. Nowak, Bull. Math. Biol. 66, 1621 (2004)
M.A. Nowak, Evolutionary Dynamics (Cambridge, MA, 2006)
P.A.P. Moran, The Statistical Processes of Evolutionary Theory (Oxford, 1962)
A. Traulsen, J.C. Claussen, C. Hauert, Phys. Rev. Lett. 95, 238701 (2005)
A. Traulsen, M.A. Nowak, J.M. Pacheco, Phys. Rev. E 74, 011909 (2006)
J.C. Claussen, A. Traulsen, Phys. Rev. Lett. 100, 058104 (2008)
L. Imhof, D. Fudenberg, M.A. Nowak, Proc. Natl. Acad. Sci. 102, 10797 (2005)
B. Sinervo, C.M. Lively, Nature 380, 240 (1996)
K.R. Zamudio, B. Sinervo, Proc. Natl. Acad. Sci. 97, 14427 (2000)
B. Kerr, M.A. Riley, M.W. Feldman, B.J.M. Bohannan, Nature 418, 171 (2002)
B.C. Kirkup, M.A. Riley, Nature 428, 412 (2004)
T. Czárán, R.F. Hoekstra, L. Pagie, Proc. Natl. Acad. Sci. 99, 786 (2002)
G. Szabó, G. Fáth, Phys. Rep. 446, 97 (2007)
M. Perc, J. Gómez-Gardeñes, A. Szolnoki, L.M. Floría, Y. Moreno, J.R. Soc, Interface 10, 20120997 (2013)
G.M. Mace et al., Biodiversity targets after 2010. Current Opinion in Environmental Sustainability 2, 3 (2010)
E. Ott, C. Grebogi, J.A. Yorke, Phys. Rev. Lett. 64, 1196 (1990)
E. Schöll, H.G. Schuster, Handbook of Chaos Control, 2nd edn. (Wiley-VCH, Weinheim, 2007)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Claussen, J.C. (2016). Evolutionary Dynamics: How Payoffs and Global Feedback Control the Stability. In: Schöll, E., Klapp, S., Hövel, P. (eds) Control of Self-Organizing Nonlinear Systems. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-28028-8_24
Download citation
DOI: https://doi.org/10.1007/978-3-319-28028-8_24
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-28027-1
Online ISBN: 978-3-319-28028-8
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)