Escape from a Riddled-Like Basin

We investigate a system described by a conservative and a dissipative map concatenation. A fat fractal forbidden net, induced by interaction between discontinuous and noninvertible properties, introduces rippled-like attraction basins of two periodic attractors. Small areas, which serve as escaping holes of a new type of crisis, are dominated by conventional strong dissipation and are bounded by the forbidden region, but only in the vicinity of each periodic point. Based on this understanding, the scaling behaviour of the averaged lifetime of the crisis is analytically and numerically determined to be <τ> ∝ (b-b₀)^γ, where b denotes the control parameter, b₀ denotes its critical threshold, and γ simeq -1.5.