Cybernetic causality: A unitary theory of causal recursion in natural and social systems

The phenomena connected with non-linear difference and differential equations are approached from a unifying point of view, offered by the general concept of causal recursion (Sections 1 and 2). After a short discussion of nilpotent causal recursions (Section 3), the properties of full causal recursions near or steadily developing states are considered in detail (Section 4). In the general case of causal recursion, a theorem based on a differential-geometric argument is proved concerning the convergence of trajectories, and an exhaustive classification of systems having causal recursion is obtained (Section 5). It gives, among some other things, a mathematical foundation to the concept of a self-steering system (as distinguished from that of a self-regulating system), applied in recent sociocybernetic analyses.