the qualitative changes of the behavior of the attractors on the whole, RA cannot reproduce the topological structure of the genuine “repeller” verbatim, and the correspondence of the bifurcations in QP-forced systems and those obtained by RA is somewhat obscure.

In this report, we propose a method to locate and to obtain the images of repellers in QP-forced logistic map system(QPLM) including those with non-trivial structures, and exhibit some of the numerical results obtained with this method. Our results are consistent with the bifurcation scenario that have been inferred from RA method or from direct observation of the attractors, and provide some novel perspective to bifurcation phenomena where various repellers are involved.

Our method is presented in section 2. We introduce an auxiliary dynamical system describing the evolution of a segment, that is given as a 1+2 dimensional skew-product map system, and describe outline of the method to identify “repeller” of the QPLM. Some details of the algorithm is given in the the appendix. Some of the numerical results obtained with this method are demonstrated in section 3, including detailed phase diagram exhibiting a complicated bifurcation structure near TDT(torus doubling termination) critical point, as well as images of repellers with 