A COMPUTATION OF BIFURCATION PARAMETER VALUES FOR LIMIT-CYCLES

This letter describes a new computational method to obtain the bifurca tion parameter value of a limit cycle in nonlinear autonomous systems. The method can calculate a parameter value at which local bifurcation s; tangent, period-doubling and Neimark-Sacker bifurcations are occurr ed by using properties of the characteristic equation for a fixed poin t of the Poincare mapping. Conventionally a period of the limit cycle is not used explicitly since the Poincare mapping needs only whether t he orbit reaches a cross-section or not. In our method, the period is treated as an independent variable for Newton's method, so an accurate location of the fixed point, its period and the bifurcation parameter value can be calculated simultaneously. Although the number of variab les increases, the Jacobian matrix becomes simple and the recurrence p rocedure converges rapidly compared with conventional methods.