Abstract
We consider systems that depend slowly on time (i.e., they drift) in such a way that the system slowly sweeps through a saddle-node bifurcation of a periodic orbit. Due to a common type of fractal basin boundary structure, such situations can often be expected to be “indeterminate” in the sense that it is fundamentally difficult to predict the eventual fate of an orbit that tracks the pre-bifurcation node attractor. We study the scaling properties of this indeterminacy; specifically, the sensitive dependence of the orbit's final attractor on the sweeping rate, and the scaling with noise amplitude of the final attractor capture probability. We believe that the characterizations we find can serve as potential experimental signatures indicating the presence of this “indeterminate” saddle-node bifurcation.
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