Non-linear dynamics of biological systems

All biological systems can be classified as open, dissipative and non-linear. This review introduces the most typical phenomena associated with non-linearity, dissipation and openness in biological systems. Namely, damped oscillations, self-oscillations, synchronisation, chaotic and noise-induced oscillations are explained, and illustrated by examples from various biological systems. The link is made between the experimentally registered activities and their mathematical counterparts with the help of the qualitative theory of ordinary differential equations. We introduce the ideas of non-linear and oscillatory thinking proposed by Mandelstam in the 1930s, and show how they can be applied to biological systems. An emphasis is made on the intuitive explanation of mathematical concepts rather than mathematical rigour.