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

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.

Complex mode-locking oscillations and Stern-Brocot derivation tree in a CSTR reaction with impulsive perturbations.

A complex mode-locking (entrainment) topology underlying the continuous stirred tank reactor reaction model subjected to impulsive perturbations is identified. Employing high-resolution stability diagrams, we exhibit the global structure of mode-locking oscillations and describe how they are interconnected and how their complexity unfolds with control parameters varying. The scenarios shown in the bi-parametric planes revealed that the skeleton of Arnold's tongues is organized according to the symmetric Stern-Brocot sum tree.