Analytical Approximation of heteroclinic bifurcation in a 1: 4 Resonance

Bifurcation of heteroclinic cycle near 1:4 resonance in a self-excited parametrically forced oscillator with quadratic nonlinearity is investigated analytically in this paper. This bifurcation mechanism leads to the disappearance of a slow flow limit cycle giving rise to frequency-locking near the resonance. The analytical approach used to approximate the bifurcation is based on a collision criterion between the slow flow limit cycle and saddles involved in the bifurcation. The amplitudes of the 1:4-subharmonic solution and the slow flow limit cycle are approximated using a double perturbation procedure and the heteroclinic bifurcation is captured applying the collision criterion. For validation, the analytical results are compared to those obtained by numerical simulations.