Robustness of stability regions of nonlinear circuits and systems under parameter variation

The behavior of stability regions of nonlinear dynamical systems subjected to parameter variation is studied in this paper. Sufficient conditions to guarantee the persistence of the stability boundary characterization under parameter variation are presented. When these conditions are violated, the stability region may undergo a bifurcation and may suffer drastic changes. In this paper, the behavior of stability region and stability boundary when the system undergoes a type-zero saddle-node bifurcation on the stability boundary is investigated. A complete characterization of these changes in the neighborhood of a type-zero saddle-node bifurcation point on the stability boundary is developed. These results are applied to the analysis of stability region of a simple Hopfield artificial neural network.