Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2003-06-26
Applied Mathematics and Computation, vol. 168, no. 1 (2005) 354-379
Nonlinear Sciences
Adaptation and Self-Organizing Systems
21 pages, 11 figures; reduced graphics to slash size, full version on Author's homepage. Minor revisions in text and reference
Scientific paper
10.1016/j.amc.2004.09.003
Based on the heuristics that maintaining presumptions can be beneficial in uncertain environments, we propose a set of basic axioms for learning systems to incorporate the concept of prejudice. The simplest, memoryless model of a deterministic learning rule obeying the axioms is constructed, and shown to be equivalent to the logistic map. The system's performance is analysed in an environment in which it is subject to external randomness, weighing learning defectiveness against stability gained. The corresponding random dynamical system with inhomogeneous, additive noise is studied, and shown to exhibit the phenomena of noise induced stability and stochastic bifurcations. The overall results allow for the interpretation that prejudice in uncertain environments entails a considerable portion of stubbornness as a secondary phenomenon.
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