Replication of chaos

We propose a rigorous method for replication of chaos from a prior one to systems with large dimensions. Extension of the formal properties and features of a complex motion can be observed such that ingredients of chaos united as known types of chaos, Devaney’s, Li-Yorke and obtained through period-doubling cascade. This is true for other appearances of chaos: intermittency, structure of the chaotic attractor, its fractal dimension, form of the bifurcation diagram, the spectra of Lyapunov exponents, etc. That is why we identify the extension of chaos through the replication as morphogenesis.To provide rigorous study of the subject, we introduce new definitions such as chaotic sets of functions, the generator and replicator of chaos, and precise description of ingredients for Devaney and Li-Yorke chaos in continuous dynamics. Appropriate simulations which illustrate the chaos replication phenomenon are provided. Moreover, in discussion form we consider inheritance of intermittency, replication of Shil’nikov orbits and quasiperiodical motions as a possible skeleton of a chaotic attractor. Chaos extension in an open chain of Chua circuits is also demonstrated.

► Replication of chaos in continuous-time dynamics is introduced. ► Hyperbolic and chaotic sets of functions are defined. ► The extension is rigorously approved for Devaney and Li-Yorke chaos. ► Simulations of attractors, bifurcation diagrams illustrate the results. ► Discussions of future investigations are provided.