Sparse Identification of Fractional Chaotic Systems based on the time-domain data

The complexity inherent in defining and computing fractional derivatives renders the development of a data-driven modeling framework for fractional-order systems more formidable than for their integer-order counterparts. This study introduces a methodology for sparsely identifying fractional chaotic systems by leveraging time-domain data to ascertain the system’s governing equations. Initially, we establish a sparse identification framework specifically tailored for fractional order systems and introduce a joint iterative thresholding method designed to identify these systems’ fractional and integer order components concurrently. Moreover, this study conducts a comparative analysis of two error criteria for model selection. It introduces a strategy predicated on minimizing the distance to balance sparsity and model fitting error optimally. To validate the efficacy and precision of the proposed methodology, numerical simulations were conducted on fractional-order Lorenz and Chua’s circuits, affirming the robustness and accuracy of our approach.