On Unstable Saddle-Node Connecting Orbit in a Planer Autonomous System

Tetsushi UETA  Hiroshi KAWAKAMI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E79-A    No.11    pp.1844-1847
Publication Date: 1996/11/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section LETTER (Special Section of Letters Selected from the 1996 IEICE General Conference)
Category: 
Keyword: 
saddle-node connecting orbit,  bifurcation,  topological classification of flows',  

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Summary: 
We found a novel connecting orbit in the averaged Duffing-Rayleigh equation. The orbit starts from an unstable manifold of a saddle type equilibrium point and reaches to a stable manifold of a node type equilibrium. Although the connecting orbit is structurally stable in terms of the conventional definition of structural stability, it is structually unstable since a one-deimensional manifold into which the connecting orbit flows is unstable. We can consider the orbit is one of global bifurcations governing the differentiability of the closed orbit.