Novel patterns in discrete Ikeda map: Quint points and complex non-quantum chirality.

Abstract

In this paper, the complex and dynamically rich distribution of stable phases in the well-known discrete Ikeda map is studied in detail. The unfolding patterns of these stable phases are described through three complementary stability diagrams: the Lyapunov stability diagram, the isoperiod stability diagram, and the isospike stability diagram. The adding-doubling complexification cascade and fascinating non-quantum chiral pairs are discovered, marking the first report of such structures in discrete mapping. The inherent symmetry of the Ikeda map also leads to the emergence of even more complex chiral formations. Additionally, the effects of initial value perturbations on stable phase topology are explored, revealing that in near-conservative states, small changes in initial conditions significantly disturb the system, resulting in the discovery of a multitude of previously hidden shrimp islands. Our findings enhance the understanding of non-quantum chiral structures within discrete systems and offer new insights into the intricate manifestations of stability and multistability in complex mappings.