3 research outputs found
Homoclinic connections and numerical integration
One of the best known mechanisms of onset of chaotic motion is breaking of heteroclinic and homoclinic connections. It is well known that numerical integration on long time intervals very often becomes unstable (numerical instabilities) and gives rise to what is called numerical chaos . As one of the initial steps to discuss this phenomenon, we show in this paper that Euler\u27s finite difference scheme does not preserve homoclinic connections
Homoclinic connections and numerical integration
One of the best known mechanisms of onset of chaotic motion is breaking of heteroclinic and homoclinic connections. It is well known that numerical integration on long time intervals very often becomes unstable (numerical instabilities) and gives rise to what is called \u27\u27numerical chaos\u27\u27. As one of the initial steps to discuss this phenomenon. we show in this paper that Euler\u27s finite difference scheme does not preserve homoclinic connections