Adaptation to the edge of chaos in the self-adjusting logistic map

Self-adjusting, or adaptive, systems have gathered much recent interest. We present a model for self-adjusting systems which treats the control parame ters of the system as slowly varying, rather than constant. The dynamics of these parameters is governed by a low-pass filtered feedback from the dyna mical variables of the system. We apply this model to the logistic map and examine the behavior of the control parameter. We find that the parameter l eaves the chaotic regime. We observe a high probability of finding the para meter at the boundary between periodicity and chaos. We therefore find that this system exhibits adaptation to the edge of chaos.