New explicit critical criterion of Hopf-Hopf bifurcation in a general discrete time system

► Report a new explicit criterion of Hopf-Hopf bifurcation without using eigenvalues. ► Its equivalence to the classical criterion using eigenvalues are rigorously proved. ► By using it, the parameter mechanism on bifurcation may be explicitly formulated. ► It is preferable for bifurcation analysis in high dimension discrete time systems.