Evolution of a ring-attractor in socio-spatial dynamics (Q1197064)

A central objective of this paper is to systematically study through numerical simulations the transitions surrounding a ring-attractor (a quasi-periodic motion) in the dynamics of a discrete map as one parameter varies within a very small neighborhood of the parameter space. The specific map used is the two-stock, two-location version of the universal map. The choice of a particular neighborhood of the parameter space is taken because it reveals the inner structure of quasi-periodicity and its bifurcations. Each metamorphosis occuring with a variation of parameter is presented on the pictures (chaos, 4-\(p\) cycle, ring-attractor, comets, spikes, curled jets, multispiral hole, black hole that is a special case of quasi-periodicity involving an infinitesimally small ring- attractor). The decline in spirals of attractor is revealed again by the decline in the value of the rotation number. A unit square is shown to contain eight possible relative stock size distributions at the two locations and all rules earlier identified in an earlier contribution [the author and \textit{M. Sonis}, Signature of chaos, Occas. Paper Series on Socio-Special Dynamics 1, No. 1, 57-74 (1990)] for one-stock, two location interactive dynamics were seemingly holding in this case, too.