Dynamical Complexities of Non-linear Physical and Biological Systems

The basic equations governing both physical and biological systems are non-linear. Therefore, it is not generally possible to obtain solutions of these systems analytically to decipher the observed complex dynamics. To understand the dynamics of a non-linear system, we use various numerical methods using computer. In this work, we use (a) power spectrum, (b) Poincaré-surface of section, (c) correlation dimension, (d) spectral and sample entropy method to understand the complex dynamics observed in simple non-linear systems, for example logistic map, Duffing oscillator, Lorenz system, Hindmarsh–Rose model in neuro-bioscience. We also describe methods to obtain visibility graph from a time series of a dynamical system and further use them to provide a network frame work for any dynamical system.