Details

Autor(en) / Beteiligte

• Li, Sheng-Hong
• Liu, Xian-Bin

Titel

The maximal Lyapunov exponent of a co-dimension two-bifurcation system excited by a bounded noise

Ist Teil von

• Acta mechanica Sinica, 2012-04, Vol.28 (2), p.511-519

Ort / Verlag

Heidelberg: The Chinese Society of Theoretical and Applied Mechanics, Institute of Mechanics, Chinese Academy of Sciences

Erscheinungsjahr

2012

Link zum Volltext

Quelle

SpringerLink (Online service)

Beschreibungen/Notizen

• In the present paper, the maximal Lyapunov ex- ponent is investigated for a co-dimension two bifurcation system that is on a three-dimensional central manifold and subjected to parametric excitation by a bounded noise. By using a perturbation method, the expressions of the invari- ant measure of a one-dimensional phase diffusion process are obtained for three cases, in which different forms of the matrix B, that is included in the noise excitation term, are assumed and then, as a result, all the three kinds of singular boundaries for one-dimensional phase diffusion process are analyzed. Via Monte-Carlo simulation, we find that the an- alytical expressions of the invariant measures meet well the numerical ones. And furthermore, the P-bifurcation behav- iors are investigated for the one-dimensional phase diffusion process. Finally, for the three cases of singular botmdaries for one-dimensional phase diffusion process, analytical ex- pressions of the maximal Lyapunov exponent are presented for the stochastic bifurcation system.