We study analytically the steady-state regime of a network of n error-prone
self-replicating templates forming an asymmetric hypercycle and its error tail.
We show that the existence of a master template with a higher non-catalyzed
self-replicative productivity, a, than the error tail ensures the stability of
chains in which m<n-1 templates coexist with the master species. The stability
of these chains against the error tail is guaranteed for catalytic coupling
strengths (K) of order of a. We find that the hypercycle becomes more stable
than the chains only for K of order of a2. Furthermore, we show that the
minimal replication accuracy per template needed to maintain the hypercycle,
the so-called error threshold, vanishes like sqrt(n/K) for large K and n<=4.