We consider a resonance 1:1 bifurcation with (Formula presented.)-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.
|Journal||Journal of difference equations and applications|
|Publication status||Published - 2 Sep 2018|
- Numerical continuation
- Critical Normal Form
- Resonance 1:1