Numerical bifurcation analysis of double +1 multiplier in ℤ₃-symmetric maps

ABSTRACT

We consider a resonance 1:1 bifurcation with ${\mathbb{Z}}_3$-symmetry in a discrete-time dynamical system. We employ standard normalization and center manifold reduction techniques. With this, we obtain the normal form up to cubic order and also explicit formulas for the critical normal form coefficients. We provide an implementation of our algorithm that can be used in the numerical bifurcation toolbox MATCONTM. We illustrate our analysis with a Cournot triopoly model from economics.

KEYWORDS:

• Resonance 1:1 (double $+1$) bifurcation
• ${\mathbb{Z}}_3$-symmetry
• map
• critical normal form coefficient
• numerical continuation

Disclosure statement

No potential conflict of interest was reported by the authors.