Noise-free Stochastic Resonance in Simple Chaotic Systems

The phenomenon of Stochastic Resonance (SR) is reported in a completely noise-free situation, with the role of thermal noise being taken by low-dimensional chaos. A one-dimensional, piecewise linear map and a pair of coupled excitatory-inhibitory neurons are the systems used for the investigation. Both systems show a transition from symmetry-broken to symmetric chaos on varying a system parameter. In the latter state, the systems switch between the formerly disjoint attractors due to the inherent chaotic dynamics. This switching rate is found to ``resonate'' with the frequency of an externally applied periodic perturbation (either parametric or additive). The existence of a resonance in the response of the system is characterized in terms of the residence-time distributions. The results are an unambiguous indicator of the presence of SR-like behavior in these systems. Analytical investigations supporting the observations are also presented. The results have implications in the area of information processing in biological systems.Comment: 12 pages LaTex, using elsart.cls. 7 figures. To appear in Physica A (1999

Stochastic Maps, Wealth Distribution in Random Asset Exchange Models and the Marginal Utility of Relative Wealth

We look at how asset exchange models can be mapped to random iterated function systems (IFS) giving new insights into the dynamics of wealth accumulation in such models. In particular, we focus on the "yard-sale" (winner gets a random fraction of the poorer players wealth) and the "theft-and-fraud" (winner gets a random fraction of the loser's wealth) asset exchange models. Several special cases including 2-player and 3-player versions of these `games' allow us to connect the results with observed features in real economies, e.g., lock-in (positive feedback), etc. We then implement the realistic notion that a richer agent is less likely to be aggressive when bargaining over a small amount with a poorer player. When this simple feature is added to the yard-sale model, in addition to the accumulation of the total wealth by a single agent ("condensation"), we can see exponential and power-law distributions of wealth. Simulation results suggest that the power-law distribution occurs at the cross-over of the system from exponential phase to the condensate phase.Comment: 7 pages, 8 figures, to appear in Phys. Scr. T (Spl. issue: Proc. Int. Conf. UASP'03

Hollywood blockbusters and long-tailed distributions: An empirical study of the popularity of movies

Numerical data for all movies released in theaters in the USA during the period 1997-2003 are examined for the distribution of their popularity in terms of (i) the number of weeks they spent in the Top 60 according to the weekend earnings, and (ii) the box-office gross during the opening week, as well as, the total duration for which they were shown in theaters. These distributions show long tails where the most popular movies are located. Like the study of Redner [S. Redner, Eur. Phys. J. B \textbf{4}, 131 (1998)] on the distribution of citations to individual papers, our results are consistent with a power-law dependence of the rank distribution of gross revenues for the most popular movies with a exponent close to -1/2.