Alexander K. Cherkashin

V.B. Sochava Institute of Geography Siberian Branch of the Russian Academy of Sciences

Metatheoretical (MT) bases of intertheoretical mathematical modeling of natural, economic and social systems are discussed. The main MT-statements are formulated in terms of differential geometry of tangent fibration and foliation on manifolds taking into account experience of creation of polysystem models in geographical science. The manifold is interpreted as the geographical environment of formation of the phenomena and processes. The equations for their modeling appear respectively as a result of mapping estimation functions upon vector fields of states and velocities of the fiber space. The tangent point of fiber contact is interpreted as environmental type of realization of the modelled regularities, and it’s global coordinates correspond to conditions of environmental shift of system parameters. Taking into account these shifts the local system of coordinates is formed. The created MT-equations of connections and changes of relative parameters don't depend on the choice of global (external) and local (internal) coordinate systems. The foliation of the environment manifolds defines topological and typological structures of a research space as geoinformation source of knowledge on heterogeneity of local conditions. MT-modeling proposes the universal equations and allows taking into account an originality of systems and their environment through content-related interpretation of abstract concepts and environmental shift of variables. For MT-modeling the structures and functions connected with fibers are of importance, in particular, trihedrons and tetrahedrons of lines and surfaces. Their analogs are formal categories as the commutative diagrams of connections of concepts generating laws of creation of any system models.

metatheoretical knowledge, intertheoretical modeling, polysystem models, environmental manifolds, environmental relativity, vector fields and functionals, equations of processes and phenomena