The onset of turbulence in discrete relative multiple spatial dynamics

摘要

The paper presents certain new results from discrete relative dynamics in bifurcation theory. These results are found in two- and three-location, one-stock interactive dynamics. They include the following: (i) the discrete-relative-dynamics analogue to the Hopf bifurcation of the continuous-dynamics case; (ii) the demonstration of “local, partial turbulence” in discrete relative dynamics; (iii) the presence of “strange containers,” equivalent to these labeled “strange attractors” in the current literature on continuous (fixed-point) processes. Result (i) is obtained and discussed in the context of a two-location, one-stock interactions; results (ii) and (iii) are presented within the framework of the three-location, one-stock discrete relative dynamic interactions. Some analytical and numerical solutions and their connections with experimental mathematics (involving numerical computations) are elaborated upon. The remaining analytical proofs and modifications to the reported results are left to the interested mathematician. Mainly, the objective here is to report these new findings.