Dynamics of the two-frequency torus breakdown in the driven double scroll circuit

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Abstract
In this work we numerically identify three scenarios for the two-frequency torus breakdown to chaos, using the driven double scroll circuit, with varying driving parameters. Two of these scenarios follow the Curry-Yorke route to chaos. For one scenario, we identify the transition to chaos through the onset of a heteroclinic tangle and its heteroclinic points. In the other scenario, chaos appears via period-doubling bifurcations. The third scenario is through the type-II intermittency for which a quasiperiodic torus grows in size, breaks by touching external saddle points, and forms a heteroclinic saddle connection. These dynamic scenarios have distinct structure evolutions: for the Curry-Yorke route, chaos appears softly and alternates with phase locking, while, for the type-II intermittency, chaos appears abruptly and is preserved for a large range of the varying driving parameter.