Scaling Law of the Mean Laminar Length in Intermittent Chaos

抄録

The mean laminar length of intermittency generated by the dynamical equation x_n+1=(1+ε)x_n+x_n^z obeys the scaling law ‹ N › ∝ ε^-γ, where γ is related to the reinjection probability through a reinjection mapping function (1-x)^m and is approximated by γ=1-1/m(z-1). This result is ascertained by numerical simulations, and for m=1 it is in agreement with the result for the random uniform reinjection probability in type-III intermittency. It is also used not only to classify the intermittent chaos but also to determine the scaling law for the mean laminar length from the analyses of the return map which is experimentally or theoretically provided.