In this paper we calculate the critical scaling exponents describing the variation of both the
positive Lyapunov exponent, λ+, and the mean residence time, τ , near the second order phase transition
critical point for dynamical systems experiencing crisis-induced intermittency. We study in detail
2-dimensional 2-parameter nonlinear quadratic mappings of the form: Xn+1 = f1(Xn, Yn; A,B) and
Yn+1 = f2(Xn, Yn; A,B) which contain in their parameter space (A,B) a region where there is crisis induced
intermittent behaviour. Specifically, the Henon, the Mira 1, and Mira 2 maps are investigated in the
vicinity of the crises.We show that near a critical point the following scaling relations hold: τ ∼ |A−Ac|−γ,
(λ+ −λ+c ) ∼| A−Ac |βA and (λ+ −λ+c ) ∼| B −Bc |βB. The subscript c on a quantity denotes its value at
the critical point. All these maps exhibit a chaos to chaos second order phase transition across the critical
point. We find these scaling exponents satisfy the scaling relation γ = βB( 1
βA
− 1), which is analogous to
Widom’s scaling law. We find strong agreement between the scaling relationship and numerical results
