Evolution of Ecosystems as Successions: Discrete Switching in Continuous Models

A process of long-term ecological successions has been considered. The model of open Eigen´s hyper cycle has been proposed for modelling of the process. The model is a system of differential equation of the second order. The multi-dimension case is analysed, it is shown that i many cases consideration of dynamics of n-dimensional system can be simplified by partial reduction to (n-1)-dimensional cases. The system´s dynamic can be considered as a self-development process, it is shown, that in the course of its development the system can choose its own dimension. Main steps of the qualitative analysis have been realised: determination of equilibrium points and their classification, complete classification of possible topologies and preparation of typical phase portraits, bifurcation analysis. The quasi-discrete dynamics of the system is explained by its bifurcation properties, produced step-by-step changing of the system structure. Ways of practical use of the model for description of biological has been discussed.