Chaos and bifurcation in numerical computation by the Runge-Kutta method
作者:
KAZUMASA HIRAI,
TOMOHIKO ADACHI,
期刊:
International Journal of Systems Science
(Taylor Available online 1994)
卷期:
Volume 25,
issue 11
页码: 1695-1706
ISSN:0020-7721
年代: 1994
DOI:10.1080/00207729408949307
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
In this paper the chaotic phenomenon and bifurcation in numerical computation using the Runge-Kutta method to discretize the nonlinear differential equation are investigated. It is shown that the bifurcation condition in the discretized equation is given by the eigenvalue of the jacobian matrix of the original differential equation. As an example, the bifurcation and chaos when a second-order nonlinear equation is discretized by the Runge-Kutta method is investigated and it is shown that the scenario from a stable fixed point to chaos when the fourth-order Runge-Kutta method is applied is quite different from those of the second-order Runge-Kutta method
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