Variation of certain statistical quantities near critical bifurcations

✍ Scribed by S. Rajasekar; V. Chinnathambi

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 356 KB
• Volume: 11
• Category: Article
• ISSN: 0960-0779
• DOI: 10.1016/s0960-0779(98)00238-0

✦ Synopsis

We study the behaviour of average value of state variable X and maximal Lyapunov exponent at various bifurcations of chaos in logistic map and Bonhoeer±van der Pol (BVP) equation. Power-law variation is observed near sudden widening and intermittency bifurcations while linear variation is found near band-merging bifurcation. The ¯uctuation of a coarse-grained coordinate n n near the critical bifurcations is characterized using its variance r n qY ÀI q I. We study the statistical dynamics of the local Lyapunov exponent K Y v and the local mean value " v of the coordinate X calculated after every L time steps. The standard deviation of K Y v and " v about their mean values is found to approach zero in the limit v 3 I as v Àb . We show abrupt variation of the scaling exponent b near the bifurcations.