Chaos in nonlinear paradoxical games

L. Drossos, T. Bountis, J. S. Nicolis

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

Paradoxical games are nonconstant sum conflicts, where individual and collective rationalities are at variance and refer to a dyadic antagonism where the contestants blackmail each other. The state space dynamics of a class of such games has been previously studied in the planar case of two variables x 1, x 2 (representing the propensities of the two parties to cooperate), for which phase space portraits have been obtained for a wide range of control parameters. In this paper, we extend the analysis to 3 dimensions, by allowing two of these parameters (the so-called «tempting factors») to oscillate in time. We observe on a Poincaré surface of section that the invariant manifolds of two unstable fixed points U 1 and U 1 intersect, and form heteroclinic and homoclinic orbits. Thus, sufficiently close to U 1 and U 2, one finds «horseshoe» chaos and extremely sensitive dependence to initial conditions. Moreover, since the equations of motion can be written in Hamiltonian form, all the known phenomena of periodic, quasi-periodic and chaotic orbits can be observed around two stable fixed points, where the two parties become «deadlocked» in an inconclusive exchange that never ends.

Original languageEnglish
Pages (from-to)155-176
Number of pages22
JournalIl Nuovo Cimento D
Volume12
Issue number2
DOIs
Publication statusPublished - Feb 1 1990

Keywords

  • General, theoretical and mathematical biophysics (including logic of biosystems, quantum biology and relevant aspects of thermodynamics, information theory, cybernetics and bionics)

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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