Computing Melnikov Curves for Periodically Perturbed Piecewise Smooth Oscillators

摘要: Curves dividing the parameter plane into regions according to presence or absence of homoclinic heteroclinic tangle corresponding periodically perturbed saddle piecewise smooth oscillator are studied using Melnikov analysis. The analysis is not simplified by choosing discontinuity at a convenient location. Separatrix unperturbed system parametrized exactly in manner. Switching times, i.e. values which separatrix crosses plane, obtained. times split integral various subintegrals evaluated either term-wise integration infinite series integrand approximately finite-term approximation integrand, latter being computationally an extensive task. Integral evaluations though approximate, purely analytical expressions terms special functions such as digamma and hypergeometric. plots show that boundary between three differ qualitatively case parametric external excitations, however; adding self-excitation one does much alter quantitatively.