Nested sequences of period-adding stability phases in a CO2 laser map proxy

Abstract

• Nested sequences of period-adding bifurcations found in Henon map. • Period-adding sequences exist in the Hamiltonian limits of the map. • Adding cascade crisscross the whole control parameter space. We report the discovery of wide nested sequences of period-adding complexification routes spawning the whole control parameter space of the Hénon map, a discrete-time proxy of single-mode loss-modulated CO 2 lasers. For a realistic map, the new adding routes found reproduce analogous phenomena previously observed in continuous-time differential equations describing, for instance, oscillatory phases in an enzyme reaction model. In contrast to differential equations, the map is analytically tractable to a large extent, and provides a prototypic framework to investigate intricate features of generic dissipative flows.