Skip to main content
SpringerLink
Log in

Selfregulation of behaviour in animal societies

III. Games between two populations with selfinteraction

  • Published:
Biological Cybernetics Aims and scope Submit manuscript

Abstract

The ordinary differential equation x = x(1 − x) (a + bx + cy) and y = y(1 − y) (d + ex + fy) is classified with the methods of topological dynamics. This equation describes the evolution of strategies in animal contests between two populations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Cowan, J.D.: Statistical mechanics of nervous nets. In: Neural networks. Caianiello, E.R. (ed.), pp. 181–188. Berlin, Heidelberg, New York: Springer 1968

    Google Scholar 

  • Cowan, J.D.: A statistical mechanism of nervous activity. In: Lectures on Mathematics in the Life Sciences. Gerstenhaber, M. (ed.), pp. 1–57. Providence, R.I.: Am. Math. Soc. 1970

    Google Scholar 

  • Eigen, M., Schuster, P.: The hypercycle — a principle of natural self-organization. Berlin, Heidelberg, New York: Springer 1979

    Google Scholar 

  • Gottlieb, R.: Diplomarbeit, Frankfurt/Main 1980

  • Hofbauer, J.: On the occurrence of limit cycles in the Volterra-Lotka differential equation. J. Non-linear Analysis (in press) (1980)

  • Hofbauer, J.: A general cooperation theorem for hypercycles. Mh. Math. (in press) (1981)

  • Kolmogoroff, A.N.: Sulla teoria di Volterra della lotta per l'esistenza. G. Istituto Ital. Attuari7, 74–80 (1936)

    Google Scholar 

  • Schuster, P., Sigmund, K.: Coyness, philandering and stable strategies. Anim. Behav. (in press) (1980)

  • Taylor, P.D.: Evolutionary stable strategies with two types of players. J. Appl. Prob.16, 76–83 (1979)

    Google Scholar 

  • Zeeman, E.C.: Population dynamics from game theory. Proc. Int. Conf. on Global Theory of Dynamical Systems, North Western University, Evanston, Ill. Preprint 1979

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Chemie und Strahlenchemie, Wien, Austria

    Peter Schuster, Karl Sigmund, Josef Hofbauer, Ramon Gottlieb & Philip Merz

  2. Institut für Mathematik der Universität Wien, Wien, Austria

    Peter Schuster, Karl Sigmund, Josef Hofbauer, Ramon Gottlieb & Philip Merz

Authors
  1. Peter Schuster
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Karl Sigmund
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Josef Hofbauer
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ramon Gottlieb
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Philip Merz
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work has been supported financially by the Austrian “Fonds zur Förderung der wissenschaftlichen Forschung”, Project Nr. 3502. Two of us, Ramon Gottlieb and Philip Merz, received a scholarship from the D.A.A.D.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schuster, P., Sigmund, K., Hofbauer, J. et al. Selfregulation of behaviour in animal societies. Biol. Cybernetics 40, 17–25 (1981). https://doi.org/10.1007/BF00326677

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00326677

Keywords

Search

Navigation