Entrainment by chaos (Q744448)

The effect of weak chaotic forcing on stable periodic oscillations is investigated in this work. Consider a system of ordinary differential equations, which supports an asymptotically stable limit cycle. Suppose it is perturbed by a small term driven by a chaotic trajectory produced by another system, called a chaotic generator. It is shown that the perturbed system inherits certain properties of the chaotic generator such as the sensitive dependence on initial data and the existence of a period-doubling cascade. The results are illustrated with numerical examples of chaotic entrainment in several oscillatory systems including a chemical oscillator, the normal form of the Andronov-Hopf bifurcation, and a Chua oscillator.