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A perturbation-incremental method for the calculation of semi-stable limit cycles of strongly nonlinear oscillators. (English) Zbl 0964.65145

The authors describe the existing qualitative results regarding the limit cycles for the nonlinear oscillator equations \(x''+g(x)=\lambda f(x,x',\mu)x'\). To apply a numerical approach, the authors transform this equation into an integral equation, then the initial solution for \(\lambda\sim 0\) is obtained by using the perturbation method. The solution for an arbitrary value of \(\lambda\) can be determined by using the incremental approach. Two examples (including the generalized Lienard equation) are demonstrated.

MSC:

65P40 Numerical nonlinear stabilities in dynamical systems
65L05 Numerical methods for initial value problems involving ordinary differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
37M05 Simulation of dynamical systems
37C75 Stability theory for smooth dynamical systems
34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations
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