Homoclinic Quasiperiodic Orbits and Emergence of Strange Nonchaotic Attractors in a Discontinuous Piecewise Smooth Map
Jicheng Duan, Laura Gardini, Zhouchao Wei, Iryna Sushko, Yiwen Chen
Source abstract
ABSTRACT This paper investigates the formation and evolution of strange nonchaotic attractors (SNAs) in a discontinuous noninvertible piecewise‐smooth map subjected to quasiperiodic forcing. The system is formulated as a two‐dimensional skew‐product, combining a piecewise‐smooth one‐dimensional base map with an irrational rotation. The notion of quasiperiodic homoclinic and heteroclinic orbits is introduced, and their potential relevance to the transition from smooth tori to SNAs is explored. Forward images of critical lines are shown to reflect key changes in the attractor and its basin, including disconnected components and the formation of holes. Discontinuities in the attractor are found to result from direct contact with the discontinuity line of the map. Through a set of representative examples, we identify three main routes to SNA formation: (i) contact between the attractor and its basin boundary leading to homoclinic orbits, (ii) contact between the attractor and a repeller, leading to homoclinic orbits, and (iii) contact between the attractor and the discontinuity set. These results clarify how different types of critical curves shape the dynamics, and contribute to the understanding of attractor evolution in discontinuous noninvertible quasiperiodically forced systems.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.