Heteroclinic connections in the 1:4 resonance problem using nonlinear transformation method

In this paper, the method of nonlinear time transformation is applied to obtain analytical approximation of heteroclinic connections in the problem of stability loss of self-oscillations near 1:4 resonance. As example, we consider the case of parametric and self-excited oscillator near the 1:4 subharmonic resonance. The method uses the unperturbed heteroclinic connection in the slow flow to determine conditions under which the perturbed heteroclinic connection persists. The results show that for small values of damping, the nonlinear time transformation method can predict well both the square and clover heteroclinic connection near the 1:4 resonance. The analytical finding is confirmed by comparisons to the results obtained by numerical simulations.