Classification of Invariant Sets and Global Behavior of Third Order Nonlinear Systems
Summary :
In this paper we deal with a class of nonlinear differential equations which arise in physical systems. Up to the present time no proper generalized classification of invariant sets with high dimension has been proposed. Invariant sets under the Poincaré transformation are classified into 2H -types according to the characteristic of their adjacent manifolds, where H is a hyperbolicity defined in the neighborhood of the invariant sets. In the final section of this paper, we apply the reduced classification of invariant sets to the third order nonlinear systems which are derived from parametric excitation circuits and discussed their global behavior of invariant sets and manifolds in the topological space. Doubly asymptotic points, homoclinic and heteroclinic types, located in the three-dimensional space are also obtained.
- Publication
- IEICE TRANSACTIONS on transactions Vol.E69-E No.6 pp.732-739
- Publication Date
- 1986/06/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Nonlinear Problems
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Norio AKAMATSU, "Classification of Invariant Sets and Global Behavior of Third Order Nonlinear Systems" in IEICE TRANSACTIONS on transactions,
vol. E69-E, no. 6, pp. 732-739, June 1986, doi: .
Abstract: In this paper we deal with a class of nonlinear differential equations which arise in physical systems. Up to the present time no proper generalized classification of invariant sets with high dimension has been proposed. Invariant sets under the Poincaré transformation are classified into 2H -types according to the characteristic of their adjacent manifolds, where H is a hyperbolicity defined in the neighborhood of the invariant sets. In the final section of this paper, we apply the reduced classification of invariant sets to the third order nonlinear systems which are derived from parametric excitation circuits and discussed their global behavior of invariant sets and manifolds in the topological space. Doubly asymptotic points, homoclinic and heteroclinic types, located in the three-dimensional space are also obtained.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e69-e_6_732/_p
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@ARTICLE{e69-e_6_732,
author={Norio AKAMATSU, },
journal={IEICE TRANSACTIONS on transactions},
title={Classification of Invariant Sets and Global Behavior of Third Order Nonlinear Systems},
year={1986},
volume={E69-E},
number={6},
pages={732-739},
abstract={In this paper we deal with a class of nonlinear differential equations which arise in physical systems. Up to the present time no proper generalized classification of invariant sets with high dimension has been proposed. Invariant sets under the Poincaré transformation are classified into 2H -types according to the characteristic of their adjacent manifolds, where H is a hyperbolicity defined in the neighborhood of the invariant sets. In the final section of this paper, we apply the reduced classification of invariant sets to the third order nonlinear systems which are derived from parametric excitation circuits and discussed their global behavior of invariant sets and manifolds in the topological space. Doubly asymptotic points, homoclinic and heteroclinic types, located in the three-dimensional space are also obtained.},
keywords={},
doi={},
ISSN={},
month={June},}
Copy
TY - JOUR
TI - Classification of Invariant Sets and Global Behavior of Third Order Nonlinear Systems
T2 - IEICE TRANSACTIONS on transactions
SP - 732
EP - 739
AU - Norio AKAMATSU
PY - 1986
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E69-E
IS - 6
JA - IEICE TRANSACTIONS on transactions
Y1 - June 1986
AB - In this paper we deal with a class of nonlinear differential equations which arise in physical systems. Up to the present time no proper generalized classification of invariant sets with high dimension has been proposed. Invariant sets under the Poincaré transformation are classified into 2H -types according to the characteristic of their adjacent manifolds, where H is a hyperbolicity defined in the neighborhood of the invariant sets. In the final section of this paper, we apply the reduced classification of invariant sets to the third order nonlinear systems which are derived from parametric excitation circuits and discussed their global behavior of invariant sets and manifolds in the topological space. Doubly asymptotic points, homoclinic and heteroclinic types, located in the three-dimensional space are also obtained.
ER -
English
