On perturbation procedure for limit cycle analysis

摘要: Abstract In the use of perturbation procedure for analysing limit cycle an autonomous system, people usually assumed initial condition ẋ(0) = 0. However, this is often simplified to x nh (0) 0, (n= 1, 2,…) and taken as additional determine a constant, say bn, homogeneous solution xn cosτ + bn sin τ equation each order. Nevertheless, commonly accepted will lead large errors, especially case larger values parameter e. paper, constant phase angle On in solutions xnh Ancos (τ On) (n adopted, i.e. O1 O2 … O. The cycles obtained by present corresponding are good agreement with numerical results Runge-Kutta integration, analytical expression incremental harmonic balance method even e 1.