ABSTRACT
This chapter presents the results of stability analysis applied to models of multispecies community dynamics, which were originated in the works of A. Lotka and V. Volteira. The first logical step in studying a community of several interacting species, so common in ecology, is a description of the structure of interactions among species by means of a graph. Vertices of the graph represent individual species or whole groups of species if they play the same role in the structure. The quantitative information, in a special form, is contained in the so-called community matrix, which also represents the structure of intraspecies and (pair-wise) interspecies relations and plays an important role in studying multispecies communities. Due to the uniqueness and global stability of equilibrium, Lotka-Volterra dissipative systems can be regarded as multidimensional analogs to the logistic dynamics of a single population, where exponential growth is stabilized by intraspecies regulation.
