Bat algorithm for attractor reconstruction of low-dimensional chaotic maps from time series

Abstract

Reconstructing the attractors of unknown chaotic systems from time series data presents a formidable challenge with broad applications across various disciplines. In this paper, we propose a swarm intelligence approach to address this challenge, focusing specifically on low-dimensional chaotic maps. Our approach is based on the bat algorithm, a renowned bio-inspired optimization technique well-suited for continuous optimization tasks. We evaluate the effectiveness and validity of our proposed approach by applying it to two distinct examples of chaotic maps: the Burger map and the Duffing map. Through comprehensive experimentation, we showcase the satisfactory performance of our method in reconstructing attractors from time series data. Based on our empirical findings, we conclude that our approach holds significant promise for the reconstruction of attractors of low-dimensional chaotic maps using time series data.