Summary: We present a nonlinear discrete dynamical model of investment competition with imperfect information for 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.
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