Abstract
The dynamical behavior of a one-dimensional inelastic particle system is investigated. By the means of map and spatial-temporal pattern we find the chaotic motion and the periodic motion in this simple system. We characterize several kinds of transitions and introduce the idea of a small collision chain to explain the universal relation ${n=N}^{2}$ between the number of collisions in a cycle n and the number of the particles N of the system for period-1 behavior.
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