Approximate discrete dynamics of EMG signal

TL;DR

This paper investigates the chaotic nature of Electromyography (EMG) signals by reconstructing attractors and Poincare maps, demonstrating that a 2D Poincare map can effectively describe the signal's complex dynamics.

Contribution

It introduces a method to reconstruct attractors from EMG signals and shows that suitable Poincare sections can produce chaotic or non-chaotic 2D maps, revealing underlying dynamics.

Findings

EMG signals exhibit chaotic attractors.

A 2D Poincare map can be constructed for EMG signals.

Different Poincare sections yield maps with varying chaos properties.

Abstract

Approximation of a continuous dynamics by discrete dynamics in the form of Poincare map is one of the fascinating mathematical tool, which can describe the approximate behaviour of the dynamics of the dynamical system in lesser dimension than the embedding diemnsion. The present article considers a very rare biomedical signal like Electromyography (EMG) signal. It determines suitable time delay and reconstruct the attractor of embedding diemnsion three. By measuring its Lyapunov exponent, the attractor so reconstructed is found to be chaotic. Naturally the Poincare map obtained by corresponding Poincare section is to be chaotic too. This may be verified by calculation of Lyapunov exponent of the map. The main objective of this article is to show that Poincare map exists in this case as a 2D map for a suitable Poincare section only. In fact, the article considers two Poincare sections of the attractor for construction of the Poincare map. It is seen that one such map is chaotic but the other one is not so, both are verified by calculation of Lyapunov exponent of the map.