Dynamics of a prey-predator model using sparse identification: A Data Driven Approach

Addison, L. M.

10.1166/jcsmd.2017.1139

Journal of Coupled Systems and Multiscale Dynamics

2018

2

5

143-150

Multi-scale dynamics are present within many systems in such fields as biology, epidemiology, fluid dynamics, economics and finance. Many deterministic systems generate time series data, where, in some cases, underlying equations are unknown or difficult to find. These systems are inherently noisy and high-dimensional, which induce a series of complexities. In some cases, especially in finance, robust time-series data may be sparse and difficult to analyse. This work uses a data-driven approach involving sparse regression to reconstruct a system of ordinary differential equations for a prey-predator model. The Sparse Identification of Nonlinear Dynamics (SINDy) algorithmic method is used to construct a sparse representation of the dynamical system. Here, sparse regression determines the smallest number of functions possible in the function space to generate the dynamical system. Numerical simulations are used to demonstrate the effectiveness of the approximation in different scenarios related to a financial-type prey-predator model.

Published