Self-similarity of the bandcount adding structures: Calculation by map replacement

Recently it has been demonstrated that the domain of robust chaos close to the periodic domain, which is organized by the period-adding structure, contains an infinite number of interior crisis bifurcation curves. These curves form the so-called bandcount adding scenario, which determines the occurrence of multi-band chaotic attractors. The analytical calculation of the interior crisis bifurcations represents usually a quite sophisticated and cumbersome task. In this work we demonstrate that, using the map replacement approach, the bifurcation curves can be calculated much easier. Moreover, using this approach recursively, we confirm the hypothesis regarding the self-similarity of the bandcount adding structure.