Homotopy Method of Calculating Bifurcating Solutions for Infinite Dimensional Chaotic Systems

Mitsunori MAKINO; Shin'ichi OISHI; Kazuo HORIUCHI

Homotopy Method of Calculating Bifurcating Solutions for Infinite Dimensional Chaotic Systems

Mitsunori MAKINO, Shin'ichi OISHI, Kazuo HORIUCHI

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A numerical method is proposed for identifying bifurcating solution of infinite dimensional nonlinear equations by making use of the infinite dimensional homotopy method. In this paper in the first place, in order to show the existence of bifurcating solutions for a certain class of the Fredholm operators, a mapping degree is defined which has the similar properties as in a finite dimensional space. Using this, under certain conditions a primary bifurcation point exists for a certain type of infinite dimensional nonlinear equations. Furthermore, in case of the Leray-Schauder operator, it is shown that a certain bifurcating solution of the Leray-Schauder operator equation can be identified by making use of the infinite dimensional homotopy method.

Publication: IEICE TRANSACTIONS on transactions Vol.E73-E No.6 pp.801-808

Publication Date: 1990/06/25

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Type of Manuscript: Special Section PAPER (Special Issue on Engineering Chaos)

Category: Chaos, Analysis and Numerical Method

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Mitsunori MAKINO
Shin'ichi OISHI
Kazuo HORIUCHI

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Mitsunori MAKINO, Shin'ichi OISHI, Kazuo HORIUCHI, "Homotopy Method of Calculating Bifurcating Solutions for Infinite Dimensional Chaotic Systems" in IEICE TRANSACTIONS on transactions, vol. E73-E, no. 6, pp. 801-808, June 1990, doi: .
Abstract: A numerical method is proposed for identifying bifurcating solution of infinite dimensional nonlinear equations by making use of the infinite dimensional homotopy method. In this paper in the first place, in order to show the existence of bifurcating solutions for a certain class of the Fredholm operators, a mapping degree is defined which has the similar properties as in a finite dimensional space. Using this, under certain conditions a primary bifurcation point exists for a certain type of infinite dimensional nonlinear equations. Furthermore, in case of the Leray-Schauder operator, it is shown that a certain bifurcating solution of the Leray-Schauder operator equation can be identified by making use of the infinite dimensional homotopy method.
URL: https://globals.ieice.org/en_transactions/transactions/10.1587/e73-e_6_801/_p

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@ARTICLE{e73-e_6_801,
author={Mitsunori MAKINO, Shin'ichi OISHI, Kazuo HORIUCHI, },
journal={IEICE TRANSACTIONS on transactions},
title={Homotopy Method of Calculating Bifurcating Solutions for Infinite Dimensional Chaotic Systems},
year={1990},
volume={E73-E},
number={6},
pages={801-808},
abstract={A numerical method is proposed for identifying bifurcating solution of infinite dimensional nonlinear equations by making use of the infinite dimensional homotopy method. In this paper in the first place, in order to show the existence of bifurcating solutions for a certain class of the Fredholm operators, a mapping degree is defined which has the similar properties as in a finite dimensional space. Using this, under certain conditions a primary bifurcation point exists for a certain type of infinite dimensional nonlinear equations. Furthermore, in case of the Leray-Schauder operator, it is shown that a certain bifurcating solution of the Leray-Schauder operator equation can be identified by making use of the infinite dimensional homotopy method.},
keywords={},
doi={},
ISSN={},
month={June},}

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TY - JOUR
TI - Homotopy Method of Calculating Bifurcating Solutions for Infinite Dimensional Chaotic Systems
T2 - IEICE TRANSACTIONS on transactions
SP - 801
EP - 808
AU - Mitsunori MAKINO
AU - Shin'ichi OISHI
AU - Kazuo HORIUCHI
PY - 1990
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E73-E
IS - 6
JA - IEICE TRANSACTIONS on transactions
Y1 - June 1990
AB - A numerical method is proposed for identifying bifurcating solution of infinite dimensional nonlinear equations by making use of the infinite dimensional homotopy method. In this paper in the first place, in order to show the existence of bifurcating solutions for a certain class of the Fredholm operators, a mapping degree is defined which has the similar properties as in a finite dimensional space. Using this, under certain conditions a primary bifurcation point exists for a certain type of infinite dimensional nonlinear equations. Furthermore, in case of the Leray-Schauder operator, it is shown that a certain bifurcating solution of the Leray-Schauder operator equation can be identified by making use of the infinite dimensional homotopy method.
ER -