Nonlinear stability analysis that is based on a numerical phase portrait is performed to investigate excursive instability, which is a type of Ledinegg instability, under a constant external driving force. The lumped parameter system model consists of time-dependent nonlinear ordinary differential equations, and the dynamic analysis from the lumped model agrees well with the results of previous research. A global phase portrait of excursive instability is constructed in the phase space of mass flux vs. pressure drop. The trajectories in the phase portrait accurately describe the excursive process. An initiation boundary that passes through OFI, the maximum point of the internal characteristic curve and the unstable equilibrium solution is observed and developed with a versatile expression for each operating condition. The critical margin of the perturbation intensities is quantitatively determined by the initiation boundary to evaluate the effects of perturbation intensities on the system stability. The results demonstrate that the effects of small and large perturbation intensities are different. Although a system can maintain stability under small perturbations, flow instability possibly occurs with large perturbations imposed on the system. In addition, the hysteresis phenomenon in the system with two parallel channels is observed under a constant external driving force. (C) 2019 Elsevier Ltd. All rights reserved.