The study of growth phenomena is now a dominant problem in many scientific disciplines. In macroeconomics the growth of the economy of a state is studied as a determining factor for the dynamics of national income; in the reliability of constructions, the growth of cracks plays an important role; in agriculture and the wood industry, the most important processes depend on the growth of animals and plants ; in ecology research problems deal with the increase of emissions into the air, water and

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... oil ; and growth processes are, of course, of great importance in microbiology and chemistry. Essentially, we frequently confront the opinion that we should try to control the growth rates d In x/dt of the growth indicators x. In this context, rate-coupling is considered to be the basic mechanism for all such interactions. In this monograph, we study problems of growth and structure building from the point of view of ecology. We frequently meet in the complex systems (in which we study growth phenomena), basic structures in the forms of chains and cycles. In these chains and cycles, usually the functional interaction of consecutive modules is determined by rate coupling, which means that the logarithmic derivative is something like a functional elementary operation in such systems. Using an analogy from architecture of ecological systems, we propose a Structure Design Principle. This principle yields the result that, with the help of a base module "logarithmic derivative", a large set of ordinary differential equations can be transformed into a unified description by the Lotka-Volterra equations containing, besides the original state-variables, some additional state-variables. This seems to be a remarkable step forward in the systématisation of growth processes. Important in this context is the option that we meet in objective reality only rarely uniform proportional growth ; in contrary, we encounter very often explosive growth or extinction processes in natural growth phenomena. By imbedding the Lotka-Volterra equations into the more general case of multinomial differential equations, we get a huge class of equivalence transformations admitting structural transformations for Lotka-Volterra representations. The introduction of the so-called Riccati transformation is very suitable here. It is based on the purpose to remove all autocatalytic effects from the primary Lotka-Volterra description, meaning to get rid of the diagonal elements of the interaction coefficients matrix. The Riccati representation offers some advantages : • The determination of closed analytical solutions, if such solutions exist. • A key for determination of bifurcations in simulation experiments.