Approximate discrete dynamics of EMG signal

Approximation of a continuous dynamics by discrete dynamics in the form of Poincaré 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 dimension. The present article considers a very rare biomedical signal like Electromyography (EMG) signal. It determines suitable time delay and reconstruct the attractor with embedding dimension three. By measuring its Lyapunov exponent, the attractor so reconstructed is found to be chaotic. Naturally the Poincaré map obtained by corresponding Poincaré section has 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 Poincaré map exists in this case as a 2D map for a suitable Poincaré section only. In fact, the article considers two Poincaré sections of the attractor for construction of the Poincaré 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.