Time-dependent saddle-node bifurcation: Breaking time and the point of no return in a non-autonomous model of critical transitions.

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Physica D. Nonlinear phenomena


There is a growing awareness that catastrophic phenomena in biology and medicine can be mathematically represented in terms of saddle-node bifurcations. In particular, the term "tipping", or critical transition has in recent years entered the discourse of the general public in relation to ecology, medicine, and public health. The saddle-node bifurcation and its associated theory of catastrophe as put forth by Thom and Zeeman has seen applications in a wide range of fields including molecular biophysics, mesoscopic physics, and climate science. In this paper, we investigate a simple model of a non-autonomous system with a time-dependent parameter


Institute for Systems Biology