Nontransversal curves of T-points: a source of closed curves of global bifurcations

Abstract A model is derived to explain the existence of closed bifurcation curves of homoclinic and heteroclinic connections in autonomous three-dimensional systems. This scenario is related to the failure of transversality in a curve of a certain kind of codimension-two heteroclinic loops. The predictions deduced from this model strongly agree with the numerical results obtained in a modified van der Pol–Duffing electronic oscillator.

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