Four indeterminate pitchfork bifurcations resulting in unpredictable dynamics in nonlinear driven oscillators

摘要

Subcritical pitchfork bifurcations occur when the equilibrium solution loses its stability as it intersects a secondary unstable path. In this paper we outline the phenomenon of indeterminate subcritical pitchfork bifurcations. These arise when the equilibrium solution is located on a fractal boundary as it loses its stability at the bifurcation. The outcome is then unpredictable even under infinitesimal perturbations from the equilibrium solution.