Characteristic Relations of Type-III Intermittency in an Electronic Circuit

It is reported that the characteristic relations of type-II and type-III intermittencies, with respective local Poincaré maps of $x_{n+1\mathrm{}}=(1+\epsilon )x_n{+ax}_n^3$ and $x_{n+1\mathrm{}}=-(1+\epsilon )x_n{-ax}_n^3$, are both $-\ln \left(\epsilon \right)$ 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 Letter the various characteristic relations are discussed, and the ${\epsilon }^{-1\mathrm{}/2}$ characteristic relation is obtained experimentally in an electronic circuit, with uniform reinjection probability.