Melnikov analysis of Type I subharmonic orbits in quadruple-well coupled SD oscillators
Year: 2024
Type: conference-paper
Abstract: When appropriate parameters are selected, coupled SD oscillators can exhibit bistability, tristability, and even quadrastability. The presence of multiple potential wells introduces rich dynamical characteristics into these multi-stable systems. As a result, global dynamical analysis of quad-stable systems, particularly the study of sub-harmonic orbits, has garnered significant attention in recent years. This paper aims to investigate subharmonic motion in the quad-stable system of coupled SD oscillators and to establish a theoretical framework for Melnikov analysis of Type I subharmonic orbits. Based on the derived Melnikov function, the existence of Type I subharmonic orbits is verified. Finally, numerical simulation methods are employed to validate the proposed approach by plotting phase portrait, the time history diagram t − x and spectrum diagram.
Authors: Ran Sun, Jing Li, Shaotao Zhu
Institution: Beijing University of Technology
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4405537175