Predicting Chaotic Attractor Dynamics in the Rössler System Using Deep Neural Networks: Influence of Initial Conditions and Forcing Parameters
TL;DR
This study investigates the capability of deep neural networks to infer the time-evolution of the Rössler system a canonical chaotic oscillator by leveraging initial conditions and forcing parameters as input variables and underscores the need for hybrid approaches to address long-term instability.
Abstract
Chaotic systems exhibit sensitivity to initial conditions and external parameters, posing challenges for long-term prediction. This study investigates the capability of deep neural networks (DNNs) to infer the time-evolution of the Rössler system a canonical chaotic oscillator by leveraging initial conditions (x0,y0,z0) and forcing parameters (a,b,c) as input variables. A 3D convolutional neural network (3D-CNN) architecture is designed to map these inputs to future states of the system. Results demonstrate that the DNN achieves high accuracy in short-term predictions (<50 time units) but faces exponential error growth beyond this horizon due to chaos. Notably, parameter variations (a,b,c) induce systematic shifts in attractor topology, while initial conditions amplify prediction uncertainty. The study highlights DNNs as viable tools for short-term chaotic forecasting but underscores the need for hybrid approaches to address long-term instability.