Emergence and Approximation of Tori

We will consider isolated quasi-periodic solutions and families of quasi-periodic solutions. A remarkable aspect of the system Sprott A and a few related systems is the observed presence of families of quasi-periodic solutions organised on invariant tori, a phenomenon known earlier in the context of conservative systems and the so-called KAM-theorem. We describe how the tori bifurcation phenomenon in dissipative systems has been linked to time-reversal and canards. This will be illustrated for the systems NE8 and NE9. Numerical bifurcation techniques in combination with averaging are used to study the presence of periodic and quasi-periodic solutions and possibly invariant manifolds. An interesting mechanical application will be the interaction of a parametrically excited oscillator and an oscillator with self-excitation where Hopf and Neimark–Sacker bifurcations occur naturally. This illustrates the strength of combining analytical and numerical techniques.