THE METHOD OF CAUSAL RECURSION IN MATHEMATICAL DYNAMICS: THE INTERRUPTIONS OF FEIGENBAUM BIFURCATIONS OF VERHULSTIAN ECOSYSTEMS AND OTHER APPLICATIONS

Abstract

The method of causal recursion (Section 1) is first illustrated by applications to population dynamics. As a first example the ecosystems derivable from the Verhulst axioms are analysed (Section 2). It is shown that when the total biomass becomes large enough, the system always perishes because of an interruption of the Feigenbaum scheme of bifurcations (Section 2.3). As another example of application the problem of the correct causal recursion of predator-prey ecology and the t to t + 1 map of the Hirsch-Smale model are discussed (Section 3). In Section 4 an exhaustive systemalics of causal recursions and the respective ( continuous or discontinuous) dynamical systems on an Euclidean space is given.

INDEX TERMS:

• Dynamical systems
• Feigenbaum bifurcations
• population dynamics
• systematics of systems