Riddling Crisis

A new qualitative change in chaotic dynamics caused by a collision of a chaotic attractor with the region in which points of a riddled basin of another attractor exist is illustrated and discussed. Such a change in chaotic dynamics is called a <it>riddling crisis</it>. In this case, as a parameter is varied, the destruction of the chaotic attractor occurs quite gradually, and we can observe chaotic transients for a sufficient number of iterations in a quite wide range of the control parameter. Furthermore, windows of periodic attractors appear many times after this change occurs.