Abstract
Mathematical framework is given to “resolved chaos” studied numerically by Vandermeer in population biology, which means some kind of predictability in the chaotic dynamical systems. A general theory about one-dimensional unimodal maps is constructed. A quantity called “sojourning time,” which is the duration of staying in an interval by iteration of a map, is considered. Predictability is formulated as the size of error by fluctuation from the deterministic system. Topological entropy is used as the degree of chaos and a relation between topological entropy and sojourning time is obtained. Also, some conditions for the coexistence of chaotic behavior and predictability of sojourning time are given generally. In conclusion, many of the unimodal maps with high degree of chaos are predictable on the sojourning time.
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