Synthesis of a Nonlinear Dynamical System with a Number of Prescribed Closed Orbits and Singular Points as Its Limit Sets
Summary :
The inverse problem related to nonlinear dynamical systems has received considerable attention as a basic problem concerning the construction of oscillating systems. Recently, F. Gonzaléz-Gascon, F. Moreno-Insertis, and E. Rodriguez-Camino presented an open problem on the synthesis of a two-dimensional dynamical system. We present a complete solution to the above-mentioned problem. We synthesize a structurally stable dynamical system having prescribed points and simple closed curves of class C4 as its singular points and closed orbits respectively. As to the problem above, we clarify a topological constraint which is necessary for the above-mentioned dynamical system to be synthesize. In addition, an example of a dynamical system with three closed orbits is given.
- Publication
- IEICE TRANSACTIONS on transactions Vol.E65-E No.6 pp.353-360
- Publication Date
- 1982/06/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Mathematics
Authors
Keyword
Latest Issue
Copyrights notice of machine-translated contents
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Cite this
Copy
Makoto ITOH, Tosiro KOGA, "Synthesis of a Nonlinear Dynamical System with a Number of Prescribed Closed Orbits and Singular Points as Its Limit Sets" in IEICE TRANSACTIONS on transactions,
vol. E65-E, no. 6, pp. 353-360, June 1982, doi: .
Abstract: The inverse problem related to nonlinear dynamical systems has received considerable attention as a basic problem concerning the construction of oscillating systems. Recently, F. Gonzaléz-Gascon, F. Moreno-Insertis, and E. Rodriguez-Camino presented an open problem on the synthesis of a two-dimensional dynamical system. We present a complete solution to the above-mentioned problem. We synthesize a structurally stable dynamical system having prescribed points and simple closed curves of class C4 as its singular points and closed orbits respectively. As to the problem above, we clarify a topological constraint which is necessary for the above-mentioned dynamical system to be synthesize. In addition, an example of a dynamical system with three closed orbits is given.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e65-e_6_353/_p
Copy
@ARTICLE{e65-e_6_353,
author={Makoto ITOH, Tosiro KOGA, },
journal={IEICE TRANSACTIONS on transactions},
title={Synthesis of a Nonlinear Dynamical System with a Number of Prescribed Closed Orbits and Singular Points as Its Limit Sets},
year={1982},
volume={E65-E},
number={6},
pages={353-360},
abstract={The inverse problem related to nonlinear dynamical systems has received considerable attention as a basic problem concerning the construction of oscillating systems. Recently, F. Gonzaléz-Gascon, F. Moreno-Insertis, and E. Rodriguez-Camino presented an open problem on the synthesis of a two-dimensional dynamical system. We present a complete solution to the above-mentioned problem. We synthesize a structurally stable dynamical system having prescribed points and simple closed curves of class C4 as its singular points and closed orbits respectively. As to the problem above, we clarify a topological constraint which is necessary for the above-mentioned dynamical system to be synthesize. In addition, an example of a dynamical system with three closed orbits is given.},
keywords={},
doi={},
ISSN={},
month={June},}
Copy
TY - JOUR
TI - Synthesis of a Nonlinear Dynamical System with a Number of Prescribed Closed Orbits and Singular Points as Its Limit Sets
T2 - IEICE TRANSACTIONS on transactions
SP - 353
EP - 360
AU - Makoto ITOH
AU - Tosiro KOGA
PY - 1982
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E65-E
IS - 6
JA - IEICE TRANSACTIONS on transactions
Y1 - June 1982
AB - The inverse problem related to nonlinear dynamical systems has received considerable attention as a basic problem concerning the construction of oscillating systems. Recently, F. Gonzaléz-Gascon, F. Moreno-Insertis, and E. Rodriguez-Camino presented an open problem on the synthesis of a two-dimensional dynamical system. We present a complete solution to the above-mentioned problem. We synthesize a structurally stable dynamical system having prescribed points and simple closed curves of class C4 as its singular points and closed orbits respectively. As to the problem above, we clarify a topological constraint which is necessary for the above-mentioned dynamical system to be synthesize. In addition, an example of a dynamical system with three closed orbits is given.
ER -
English
