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 Poincar\'e maps of xₙ₊₁0ex0ex=0ex0ex(1+ε)xₙ+axₙ³ and xₙ₊₁0ex0ex=0ex0ex-(1+ε)xₙ-axₙ³, are both -ln(ε) under the assumption of uniform reinjection probability. However, the intermittencies have various characteristic relations such as ε^-ν ( 1/2≤ν≤1) depending on the reinjection probability. In this Letter the various characteristic relations are discussed, and the ε^-1/2 characteristic relation is obtained experimentally in an electronic circuit, with uniform reinjection probability.