Methods of mathematical catastrophe theory in forest ecology

The quantitative prediction of restoration and age dynamics of forests is the central problem within the conception of the stable management of the resources. Forest ecosystems complexity, duration, polyvariation and non-linearity of the dynamic processes proceeding in them is reason of the absence of authentic generally accepted methods of the analysis of digressive-demutational changing (Lankin, Ivanova, 2012). In connection with this, the development of theoretico-methodological and methodical bases of the diagnostics of crisis processes and quantitative prognostification of forest dynamics is of current importance. The main factors of forest reduction in Russia are clear-cuttings and fires (Sannikov, 1992). The problem of forest restoration in the place of clear-cuttings and cuttings-burning is widely discussed in the literature. A number of hypotheses concerning mechanisms of succession changing has been suggested (Connell, Slatyer, 1977; Sannikov, 1992; Frelich, Reich, 1999). It is possible to derive quantitative forecasts of the forest ecosystem dynamics on their basis. In order to make quantitative forecasts of the formation of forest vegetation in the cuttings, the models on the base of the systems concerned with differential logistic equations (Ivanova, 2009), matrix models of competing structured populations of species-dominants (Ulanova, Zavalishin, Logofet, 2007; Logofet, 2013), as well as complex imitation models (Kellomaki et all., 1992; Meen, Nielsen, Ohlson, 2012) are being developed. Undeservedly little attention is being paid to the theory of catastrophes of R. Thoma (Thom, Zeeman, 1975) though there are examples of its successful utilization and a number of interesting conclusions has been obtained on its base (Jones, 1977; Wright, 1987; Frelich, Reich, 1999; Isaev et all., 2008; Guts, Volodchenkova, 2012).

The aim of our research is the construction, within the framework of the theory of catastrophes, of the quantitative mathematical model of forest vegetation formation afterclear-cuttings depending on two controlling parameters: intensity of grass-dwarf shrub layer development and the conditions of forest growth (soil thickness), its verification on the base of the experimental data. The main task is to develop objective quantitative methods for the appreciation of the probability of dominant-forming species changing.