New characteristic relations in type-II and III intermittency

Abstract

We obtained new characteristic relations in Type-II and III intermittencies according to the reinjection probability distribution. When the reinjection probability distribution is fixed at the lower bound of reinjection, the critical exponents are -1, as is well known. However when the reinjection probability distribution is uniform, the critical exponent is -1/2, and when it is of form 1/root x, -3/4. On the other hand, if the square root of Delta, which represents the lower bound of reinjection, is much smaller than the control parameter epsilon, i.e. epsilon much greater than Delta(1/2), critical exponent is always -1, independent of the reinjection probability distribution. Those critical exponents are confirmed by numerical simulation study.