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 Poincare maps of x(n+1) = (1 + epsilon)x(x) + ax(n)(3) and x(n+1) = -(1 + epsilon)x(n) - ax(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 less than or equal to nu less than or equal to 1) depending on the reinjection probability. In this Letter the various characteristic relations are discussed, and the epsilon(-1/2) characteristic relation is obtained experimentally in an electronic circuit, with uniform reinjection probability.