Analytical prediction of the two first period-doublings in a three-dimensional system

Analytical study of the two first period-doubling bifurcations in a three-d imensional system is reported. The multiple scales method is first applied to construct a higher-order approximation of the periodic orbit following H opf bifurcation. The stability analysis of this periodic orbit is then perf ormed in terms of Floquet theory to derive the critical parameter values co rresponding to the first and second period-doubling bifurcations. By introd ucing suitable subharmonic components in the first order of the multiple sc ale analysis the two critical parameter values are obtained simultaneously solving analytically the resulting system of two algebraic equations. Compa risons of analytic predictions to numerical simulations are also provided.