DISCONTINUOUS PATTERN OF CUMULATIVE SEPARATION BETWEEN ORBITS OF CHAOTIC TRANSIENT

The logistic map at r = 4 is modified in a narrow interval, stabilizin g a low-period unstable periodic orbit and generating transient chaos. The cumulative separation Delta between closely lying orbits is propo rtional to their initial separation epsilon for epsilon < epsilon(c), while for epsilon > epsilon(c) it is scattered within a band with epsi lon-independent average, where epsilon(c) is a critical vaIue of initi al separation. The pattern of (epsilon, Delta)-diagram is proposed for characterization of transient chaos. On the basis of these considerat ions, the concept of the uncertainty exponent is extended to the case of transient chaos. (C) 1997 Elsevier Science B.V.