Li–Yorke chaos in nonautonomous Hopf bifurcation patterns—I.

We analyze the characteristics of the global attractor of a type of dissipative nonautonomous dynamical systems in terms of the Sacker and Sell spectrum of its linear part. The model gives rise to a pattern of nonautonomous Hopf bifurcation which can be understood as a generalization of the classical autonomous one. We pay special attention to the dynamics at the bifurcation point, showing the possibility of occurrence of Li–Yorke chaos in the corresponding attractor and hence of a high degree of unpredictability. [ABSTRACT FROM AUTHOR]