Abstract: The saddle points of a dynamical system are helpful to understand the evolution of space structure. Yin et al. proposed a high-index optimization-based shrinking dimer (HiOSD) method for gradient systems to compute the index-k saddle points and construct the pathway map to help understand the structure of the energy landscape. In this talk, we will present a generalized high-index saddle dynamics (GHiSD) method for non-gradient systems. We have proved the linear stability of the index-k saddle point for the dynamics we proposed under some assumptions and demonstrated the validation of the algorithm by constructing the
solution landscape of a toy model and the phase field model in the presence of shear flow.

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