MAP DYNAMICS OF REPRODUCTION
Paul E. Phillipson, Peter M. Schuster · International Journal of Bifurcation and Chaos · 1995
One-dimensional return maps characterized by one critical point produce a universal sequence of periodic orbits, the Metropolis, Stein & Stein (MSS) sequence. Iterates of such maps can be regarded as an object whose structure is defined by the MSS sequence. The two critical point mapping [Formula: see text] as the control parameter b varies between [Formula: see text] and 1 is shown to display evolution from a single MSS structure to two identical MSS structures, suggestive of reproduction. The process of reproduction connotes a causal relationship whereby an original structure provides the blueprint for a copy. Here causality is replaced by an omniscient instruction, the mapping, and reproduction is achieved by progressively changing the instruction through variation of the control parameter. Bistability plays a crucial role in map dynamics of reproduction, which is viewed as a holistic process providing an alternative mechanism to digital replication.