Numerical Periodic Normalization for Codim 1 Bifurcations of Limit Cycles
Numerical Periodic Normalization for Codim 1 Bifurcations of Limit Cycles
Explicit computational formulas for the coefficients of the periodic normal forms for all codim 1 bifurcations of limit cycles in generic autonomous ODEs are derived. They include second-order coefficients for the fold (limit point) bifurcation, as well as third-order coefficients for the flip (period-doubling) and Neimark--Sacker (torus) bifurcations. The formulas …