A case study for homoclinic chaos in an autonomous electronic circuit: a trip taken from Takens-Bogdanov to Hopf-Sbil'nikov

Abstract The dynamics of an autonomous electronic oscillator is analysed. Both theoretical study — with methods of local bifurcation theory — and numerical simulation — by using continuation methods to detect global behaviours — are carried out. Comment is made on the presence of homoclinic connections which organise the periodic and nonperiodic behaviour. The richness and complexity of the periodic oscillations are described and the presence of isolated branches of odd-period orbits are emphasized. Further, attention is paid to the chaotic attractor coexisting with Sil'nikov homoclinicity, even in the presence of a Hopf degeneracy: the Hopf-Sil'nikov singularity.

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