Topological entropy of catalytic sets: Hypercycles revisited

摘要: The dynamics of catalytic networks have been widely studied over the last decades because their implications in several fields like prebiotic evolution, virology, neural networks, immunology or ecology. One most mathematical bodies for was initially formulated context by means hypercycle theory. is a set self-replicating species able to catalyze other replicator within cyclic architecture. Hypercyclic organization might arise from quasispecies as way increase informational containt surpassing so-called error threshold. coupling between replicators makes all behave single and coherent evolutionary multimolecular unit. inherent nonlinearities interactions are responsible emergence types dynamics, among them, chaos. In this article we begin with brief review theory focusing on its well different associated small networks. Then study properties chaotic hypercycles error-prone replication symbolic theory, characterizing, topological Markov chains, entropy periods orbits unimodal-like iterated maps obtained strange attractor. We will focus our some key parameters structure network: mutation rates, autocatalytic cross-catalytic interactions.