The description of nonautonomous bifurcation patterns is of growing interest in the scientific community, both for its theoretical interest and for its possible applications to the analysis of mathematical models. In the talk, in the wake of [1] and using results and methods of [2], conditions on the coefficients of the one-parameter family $x'(t)=\varepsilon(a(t)+b(t)\,x (t)) + c(t)\,x^2 (t) -x^3 (t)$ as $\varepsilon$ varies are established to describe the global diagram of the motion. Such conditions include the recurrency of the coefficients. Joint work with Carmen Nunez.

[1] R. Fabbri, R. Johnson, F. Mantellini, "A nonautonomous saddle-node bifurcation pattern", Stochastics and Dynamics, Vol. 4, No. 4 (2004) 335-350.

[2] J. Duenas, C. Nunez, R. Obaya, "Bifurcation theory of attractors and minimal sets in d-concave nonautonomous scalar ordinary differential equations", Journal of Differential Equations, 361 (2023) 138-182.