A non-autonomous bifurcation theory for deterministic scalar differential equations

with Rafael Obaya,
Discrete Cont. Dyn. Syst. - Ser B
  9 (3&4) (2008), 701-730.

In the extension of the concepts of saddle-node, transcritical and
pitchfork bifurcations to the non-autonomous case, one considers
the variation on the number and attraction properties of the minimal
sets for the skew-product flow determined by the initial one-parametric
equation. In this work conditions on the coefficients of the equation
ensuring the existence of a global bifurcation phenomenon of each one
of the types mentioned are established. Special attention is paid to show
the importance of the non trivial almost automorphic extensions and
pinched sets in describing the dynamics at the bifurcation point.

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