The nonlinear dynamics of response rate in FI schedules in children
Céline Clement and Jean-Claude Darcheville
Université de Lille, Ch. de Gaulle, France

The scalloped pattern observed in fixed-interval schedules (FI) in animals is highly variable.The nonlinear dynamical system model developed by Hoyert (1992) is able to generate this variability. The model also accounts for within- and between-interval variability in pigeons more accurately than any other model. We asked whether Hoyert's model could be extended to human performance; in particular, whether it could help us understand behavioral variability in temporal tasks. Eight children (mean age 4 years and 11 months) were trained on fixed-interval schedules (FI10 s, FI 20 s, FI 40 s). The operant response consisted of touching an illuminated location on a touch-sensitive screen, and the reinforcer consisted of a 20-s long cartoon. Using the nonlinear dynamics methods proposed by Hoyert---phase space, Poincaré sections, return maps---we found that the dynamics of behavior is stable within subjects, between subjects, and between FI conditions. In a dynamical system, this stability characterizes an attractor. Furtheremore, the return maps were highly ordered, which means that variability is produced by the system. These findings are a first step toward a comprehensive model of FI performance in children.

Keywords: children, fixed-interval schedule, non linear dynamics, reinforcement
contingencies, variability

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