Synchronization, intermittency and critical curves in a duopoly game

被引:102
作者
Bischi, GI
Stefanini, L
Gardini, L [1 ]
机构
[1] Univ Brescia, Dipartimento Metodi Quantitat, I-25122 Brescia, Italy
[2] Univ Urbino, Ist Sci Econ, I-61029 Urbino, Italy
关键词
synchronization; riddled basins; critical curves; contact bifurcations; duopoly games;
D O I
10.1016/S0378-4754(97)00100-6
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
The phenomenon of synchronization of a two-dimensional discrete dynamical system is studied for the model of an economic duopoly game, whose time evolution is obtained by the iteration of a noninvertible map of the plane. In the case of identical players the map has a symmetry property that implies the invariance of the diagonal x(1)=x(2), so that synchronized dynamics is possible. The basic question is whether an attractor of the one-dimensional restriction of the map to the diagonal is also an attractor for the two-dimensional map, and in which sense. In this paper, a particular dynamic duopoly game is considered for which the local study of the transverse stability, in a neighborhood of the invariant submanifold in which synchronized dynamics takes place, is combined with a study of the global behavior of the map. When measure theoretic, but not topological, attractors are present on the invariant diagonal, intermittency phenomena are observed. The global behavior of the noninvertible map is investigated by studying of the critical manifolds of the map, by which a two-dimensional region is defined that gives an upper bound to the amplitude of intermittent trajectories. Global bifurcations of the basins of attraction are evidenced through contacts between critical curves and basin boundaries. (C) 1998 IMACS/Elsevier Science B.V.
引用
收藏
页码:559 / 585
页数:27
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