Data-driven enhancement of the Hastings–Powell model using sparse identification algorithm

Abstract

A significant challenge in various fields of science and engineering is extracting governing equations from data. Prey-predator models are particularly complex due to their nonlinear behavior, making traditional analytical methods insufficient for accurately capturing their dynamics. In this study, we introduce a data-driven approach to model the intricate dynamics of Hastings–Powell model solely from time series data. This article explores the application of the sparse identification of nonlinear dynamics (SINDy) and its extension, the SINDy-PI (parallel, implicit) method, in a model representing a chaotic food chain. The main goal is to determine the governing equations that describe the chaotic dynamics of the prey-predator populations. Hence, this study uses the parameters wherein the dynamics exhibit chaotic behavior. The method of SINDy was developed with the aim of identifying governing equations of nonlinear dynamical systems. In both methods, a library of potential terms are created and then a regression problem is solved. We have employed both methods as our model incorporates not only nonlinear terms but also rational terms. Our results shows that SINDy method is unable to find the exact form of governing equations but SINDy-PI method has the capability to accurately capture the authentic structure of the governing equations. In addition, we applied model selection techniques to identify the most parsimonious model possible. Through the application of SINDy and SINDy-PI, this research contributes to the advancement of data-centric approaches in ecological modeling, offering insights into the intricate dynamics of multi-species interactions within ecosystems. Further, for this study to be more realistic, utilizing real-world data from three-species would have been ideal. However, due to non-availability of three species real data, simulated data set has been used for validation purpose.