Another Case of Degenerated Discrete Chenciner Dynamic System and Economics

Abstract

The non-degenerate Chenciner bifurcation of a discrete dynamical system is studied using a transformation of parameters which must be regular at the origin of the parameters (the condition CH.1 of the well-known treatise of Kuznetsov). The article studies a complementary case, where the transformation is no longer regular at the origin, representing a degeneration. Four different bifurcation diagrams appear in that degenerated case, compared to only two in the non-degenerated one. Degeneracy may cause volatility in economics systems modeled by discrete Chenciner dynamical systems.

Keywords

• bifurcation
• discrete-time systems
• Chenciner
• degeneracy