STABILIZATION OF CHAOS OR SUPPRESSION OF CHAOS IN A DISCONTINUOUS CIRCLE MAP

With a model relaxation oscillator and its corresponding discontinuous map,we show that the covering effect of the transient set can produce three kinds of regions:(1) stable chaotic region where all the possible periodic windows are erased,therefore chaotic trajectories are structurally stable;(2) complete phase locking region where chaos is suppressed,only periodic motion is permitted;(3) quasiperiodic region where chaos is suppressed,only quasiperiodic motion or periodic motion with marginal stability is allowed.These ideas are then used to explain the observed stable chaotic regions and the complete phase locking regions in a practical electronic relaxation oscillator.