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

Tetsushi UETA; Hiroshi KAWAKAMI

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

Tetsushi UETA, Hiroshi KAWAKAMI

Full Text Views

0

Share
Cite this

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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E79-A No.11 pp.1844-1847

Publication Date: 1996/11/25

Publicized

Online ISSN

DOI

Type of Manuscript: Special Section LETTER (Special Section of Letters Selected from the 1996 IEICE General Conference)

Category

Cite this

Copy

Tetsushi UETA, Hiroshi KAWAKAMI, "On Unstable Saddle-Node Connecting Orbit in a Planer Autonomous System" in IEICE TRANSACTIONS on Fundamentals, vol. E79-A, no. 11, pp. 1844-1847, November 1996, doi: .
Abstract: 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.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/e79-a_11_1844/_p

Copy

@ARTICLE{e79-a_11_1844,
author={Tetsushi UETA, Hiroshi KAWAKAMI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On Unstable Saddle-Node Connecting Orbit in a Planer Autonomous System},
year={1996},
volume={E79-A},
number={11},
pages={1844-1847},
abstract={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.},
keywords={},
doi={},
ISSN={},
month={November},}

Copy

TY - JOUR
TI - On Unstable Saddle-Node Connecting Orbit in a Planer Autonomous System
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1844
EP - 1847
AU - Tetsushi UETA
AU - Hiroshi KAWAKAMI
PY - 1996
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E79-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 1996
AB - 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.
ER -