Lyapunov functions as a measure of biodiversity: theoretical background

The concept of indicators (measure) of biological diversity is rather recent. Indicators of biological diversity are biased strongly towards species and away from the ecosystem as a whole, and that further progress towards generalized indicators of biological diversity poses substantial difficulties. An indicator may be a species, a structure, a process or some other feature of biological system, the occurrence of which insures the maintenance or restoration of the most important aspects of biodiversity for that system. ogical community consists of a collection of species and the underlying food web, i.e. the network of interactions by which consumers exploit and compete for available resources. The classical Lotka–Volterra model has been altered in many ways to model food webs more realistically. The dynamics of the web is mathematically described as a set of coupled non-linear ordinary differential equations. This makes application of the theory of non-linear dynamics systems possible. Commonly used models for food chains have been studied intensively using in particularly method of Lyapunov functions. In this report I introduce fitness-like and entropy-like Lyapunov functions as a basis for biodiversity study.