• DOI:10.1007/BF01188093
• Corpus ID: 119685309

Persistence of the saddle-node bifurcation for nonlinear systems with slow unmodeled dynamics

@article{FekihAhmed1993PersistenceOT,
  title={Persistence of the saddle-node bifurcation for nonlinear systems with slow unmodeled dynamics},
  author={Lazhar Fekih-Ahmed and H. D. Chiang},
  journal={Circuits, Systems and Signal Processing},
  year={1993},
  volume={12},
  pages={533-555},
  url={https://api.semanticscholar.org/CorpusID:119685309}
}

• L. Fekih-Ahmed, H. Chiang
• Published 1 December 1993
• Mathematics, Engineering, Physics
• Circuits, Systems and Signal Processing

This paper investigates the robustness of the saddle-node bifurcation for nonlinear systems under the addition of slow unmodeled dynamics. The robustness is examined in terms of existence and system behavior after bifurcation. Under fairly general conditions, it is shown that if the reduced model of a physical system encounters a saddle-node bifurcation due to a varying parameter, then the original model which includes small unmodeled dynamics will also encounter a saddle-node bifurcation. An… 

This paper investigates the robustness of the saddle-node bifurcation for nonlinear systems under the addition of slow unmodeled dynamics. The robustness is examined in terms of existence and system behavior after bifurcation. Under fairly general conditions, it is shown that if the reduced model of a physical system encounters a saddle-node bifurcation due to a varying parameter, then the original model which includes small unmodeled dynamics will also encounter a saddle-node bifurcation. An error bound is derived between the bifurcation values and the bifurcation points of the reduced model and that of the original model. Furthermore, it is shown that the dynamics after the saddle-node bifurcation of the reduced model and that of the original model are approximately the same. The persistence and non-persistence of saddle-node bifurcations are illustrated by several examples.