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The algorithm of bifurcation points forecasting in the analitical researches of complex agro-ecological systems

Osypenko V.

ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes

2012

Vol. 1, No 2

35-38

An original development is described in this work of the forecasting of so-called rare events concerning the agro-ecological systems. Under defi nition "rare" it is necessary to understand events which take place during some observed process, time intervals between them are so great that it is possible to consider that they practically do not infl uence each other. The beginning of the rare events can be called as a "bifurcation point" of the observed process. Both the multistage procedure of the forecasting based on principles of inductive modeling and the selection criterion of the best forecasting models are described.

Principles of bone remodelling - the limit cycles of bone remodelling

Petrtyl M., Danešová J.

Acta of Bioengineering and Biomechanics

2001

Vol. 3, nr 1

75-91

The bone tissue remodelling is a relatively slow process. In physiologically "normal" conditions, it tends towards the state of remodelling equilibrium. In the state of final remodelling equilibrium, the strain energy reaches its minimum. In the life of each human being, the bone tissue passes through the repeating limit cycles of its development, functioning and destruction. The paper presented is aimed at the biomechanochemical processes within one limit cycle of bone remodelling using the stoichiometric equations and kinetic equations. Each limit cycle of the bone tissue remodelling (in its assumed volume element) consists of several stages, in which the biochemical reactions are proceeding in a highly intensive way, and of several periods in which the tissue is in weakly steady states (i.e.. the biochemical reactions are very slow or they almost do not take place). Generally, throughout the life of a human, a bone tissue is several times in the principal weakly steady state, i.e., in such a state in which the long-term remodelling equilibrium is reached. This period lasts for several years (roughly for 6-8 years) in the life of an adult human in his/her productive age, while in the life of a child this period is shorter. Figuratively speaking, the stages of the bone tissue remodelling (during one limit cycle) can be compared to the tissue "childhood and maruraiion" (i.e., n stage of remodelling - apposition of the tissue), and "aging-demise" (I stage of remodelling - resorption). One limit cycle of the bone tissue life (out of the series of the subsequent periodic limit cycles) that is characterized by the bone tissue development, functioning and destruction (in the unit volume element) can be synoptically, and in the real time, described by four stages. The limit cycle is a close trajectory of solution of kinetic equations of bone remodelling. The bone tissue (in its unit volume element) passes through the repeating harmonic limit cycles (i.e., the stable periodic processes) of its development and destruction.