Predicting bifurcation points via extreme learning machine methods trained on time-series datasets and parameters in discrete dynamical systems

This paper proposes a data-driven method for obtaining the bifurcation points of a system utilizing a method based on Extreme Learning Machine with input parameter channels (ELM-IPC) trained on the time-series datasets from discrete dynamical systems. The input parameter channels permit the proposed method to align the original parameter spaces of the time-series datasets with the derived parameter spaces of the ELM-IPC model; this results in the accurate analysis of the bifurcation points of a system. To demonstrate the effectiveness of this approach, we apply it to two discrete dynamical systems: the two-dimensional Hénon map and the four-dimensional system comprising two conservatively coupled Hénon maps. Our results indicate that it is possible to obtain the bifurcation points of a system even in parameter spaces where multiple solutions coexist or periodic solutions with periods exceeding 100 are present.