Blackwell Reference Online

Extract

The theory of dynamic systems enables us to develop a dynamic point of view in communication systems and to recognize the importance of the force fields to which the members of a group in interaction are subject. Family processes, which are products of interaction between consanguine and affiliated persons, can thus be grasped in terms of dynamic systems. In such processes, biological and cultural forces are led to interact, to enter into conflict, to tend towards limit points. Let F be a system considered as a topological space . Let U be the control space. The phenomenological appearance of the state of the system varies if the point which represents the system meets a closed space, K , in U , termed by Thom (1972, pp. 335–43) the catastrophe set . That topological space will have several properties. It will have properties of differentiable structure (Euclidian space of n dimensions, i.e. R n , also called a differentiable manifold : this is a set of multi-dimensional maps, differentiable or integrable, completely covering the space of the system under consideration). This manifold enables us to study the accidents and regularities of the system, the critical points and the points of bifurcation, appearing for precise values of the derivatives of order 1, 2 … or n (See also family maps ). There will also be dynamic properties : this manifold possesses a dynamic, ... log in or subscribe to read full text