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The complexity of an investment competition dynamical model with imperfect information in a security market. (English) Zbl 1198.91123

Summary: We present a nonlinear discrete dynamical model of investment competition with imperfect information for $N$ heterogeneous oligopolists in a security market. In this paper, our focus is on a given three-dimensional model which exhibits highly rich dynamical behaviors. Based on Wen’s Hopf bifurcation criterion and Kuznetsov’s normal form theory, we study the model’s stability, criterion and direction of Neimark-Sacker bifurcation. Moreover, we numerically simulate a complexity evolution route: fixed point, closed invariant curve, double closed invariant curves, fourfold closed invariant curves, strange attractor, period-3 closed invariant curve, period-3 2-tours, period-4 closed invariant curve, period-4 2-tours.

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

##### MSC:
 91B55 Economic dynamics 37N40 Dynamical systems in optimization and economics 39A33 Complex (chaotic) behavior of solutions (difference equations)