Unconventional tipping and wrinkled hysteresis loop in nonsmooth biophysical systems

초록

A tipping point in nonlinear dynamical systems was previously understood as an abrupt transition from a high to a low stable steady state as a bifurcation parameter crosses a critical value. We uncover an unconventional tipping phenomenon in a class of non-autonomous nonsmooth biophysical systems, where the transition occurs through an intermediate, oscillatory state. Such a "stepping-stone" state also occurs in the reverse process of recovery, resulting in a "wrinkled" hysteresis loop. The dwelling time in the oscillatory state, e.g., the transient tipping time before the system settles in the low steady state, depends on the rate of the parameter change. The scaling laws of the transient tipping and recovery times are derived analytically. The intermediate state presents an opportunity for control intervention to prevent a healthy system from collapsing into a diseased state.

키워드