  In the 1990s, after a series of experiments, the behavioral psychologist and
economist Daniel Kahneman and his colleagues formulated the following Peak-End
evaluation rule: "The remembered utility of pleasant or unpleasant episodes is
accurately predicted by averaging the Peak (most intense value) of instant
utility (or disutility) recorded during an episode and the instant utility
recorded near the end of the experience", (D. Kahneman et al., 1997, QJE, p.
381). Hence, the simplest mathematical model for time evolution of the
experienced utility function $u=u(t)$ can be given by the scalar differential
equation $u'(t)=a u(t) + b \max \{u(s) : s\in [t-h,t]\}+f(t) \ (*),$ where $f$
represents exogenous stimuli, $h$ is the maximal duration of the experience,
and $a, b \in \mathbb R$ are some averaging weights. In this work, we study
equation $(*)$ and show that, for a range of parameters $a, b, h$ and a
periodic sine-like term $f$, the dynamics of $(*)$ can be completely described
in terms of an associated one-dimensional dynamical system generated by a
piece-wise continuous map from a finite interval into itself. We illustrate our
approach with two examples. In particular, we show that the hedonic utility
$u(t)$ (`happiness') can exhibit chaotic behavior.
