Modeling of evolution nonlinear ecosystem

Abstract

The term «synergy», introduced in scientific literature by G. Haken, means «joint action, selforganization, the special effects of the joint action in complex systems». Synergetics as a methodology considers irreversibility as a condition for the development of systems, and the "imbalance" of systems as an imperative of development, and this is its fundamental difference from cybernetics, from the theory of operations research and from the general theory of systems. Synergy is usually called mathematical dialectics. The theory of synergetics and the theory of self-organization, in contrast to dialectics, have a powerful formalization apparatus, a set of basic and derivative models, including in the form of differential equations in time derivatives of the second order, in the form of fractals with fractional dimension, hamiltonians, taking into account the prehistory and long memory, mathematical models taken from the theory of bifurcations. The purpose of synergetics – the identification of general ideas, general methods and general laws in various fields of natural science.
At the same time new concepts have been developing about dissipative structures generating under no equilibrium conditions as a result of the exchange of energy (and substance) with the environment when approaching the external energy to the material. This scientific direction was headed by I.R. Prigogine. Nonlinear Science opens up new possibilities in the study of the conduct of real complex dynamic ecosystems. Nonlinear dynamics is a new science studying the evolution of the real nonlinear ecosystems, where along with determinism appears dynamic chaos. Shows the role of mathematical modeling in the study of nonlinear ecologic systems. Evolutionary change in complex ecosystems due to the phenomenon of self-organization and are associated with a decrease in entropy, which is achieved by the increasing complexity of the structural organization of the ecosystem.