Characteristic Relations of Type-III Intermittency in an Electronic Circuit

Abstract

It is reported that the characteristic relations of type-II and type-III intermittencies, with respective local Poincar$\acute{e}$ maps of $x_{n+1}=(1+\epsilon )x_n+a{x}_n^3$ and $x_{n+1}=-(1+\epsilon )x_n-a{x}_n^3$, are both $-ln(\epsilon )$ under the assumption of uniform reinjection probability. However, the intermittencies have various characteristic relations such as ${\epsilon }^{-\nu }$ ($1/2\le \nu \le 1$) depending on the reinjection probability. In this Letters the various characteristic relations are discussed, and the ${\epsilon }^{-1/2}$ characteristic relation is obtained experimentally in an electronic circuit, with uniform reinjection probability.

11 pages, 5 figures. to appear in Phys. Rev. Lett