Narrow Results

Based on the results of existing studies of the minority game, we further explored the periodic properties of the time series of population and discovered its exhibition of a separate three-bump distribution, in which an unusual periodic pattern is existent. By defining "the variance of scores" of all the strategies, we found a method to identify the distinctive features between periodic and non-periodic distributions. We also found there exists a critical point at which periodic behavior disappears when N goes from large to small.

In this paper, we analyze a rather simple system in which some substance is being stored, released, and replenished simultaneously in some interdependent way. We investigate the dynamic behavior of such a system, using a two-dimensional map-based discrete-time model, and derive an integrated dynamical scene for this model. More specifically, we show the existence of an invariant curve induced by the well-known Neimark–Sacker bifurcation corresponding to the presence of a periodically oscillating behavior in this model.

Emergent behavior in interconnected systems (complex systems) is of fundamental significance in natural and engineering sciences. A commonly investigated problem is how complicated dynamics take place in dynamical systems consisting of (often simple) subsystems. It is shown though numerical experiments that emergent order such as periodic behavior can likely take place in coupled chaotic dynamical systems. This is demonstrated for the particular case of coupled chaotic continuous time Hopfield neural networks. In particular, it is shown that when two chaotic Hopfield neural networks are coupled by simple sigmoid signals, periodic behavior can emerge as a consequence of this coupling.