Melnikov analysis of Type I subharmonic orbits in quadruple-well coupled SD oscillators

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.