  Circadian rhythms in mammals are controlled by the neurons located in the
suprachiasmatic nucleus of the hypothalamus. In physiological conditions, the
system of neurons is very efficiently entrained by the 24-hour light-dark
cycle. Most of the studies carried out so far emphasize the crucial role of the
periodicity imposed by the light dark cycle in neuronal synchronization.
Nevertheless, heterogeneity as a natural and permanent ingredient of these
cellular interactions is seemingly to play a major role in these biochemical
processes. In this paper we use a model that considers the neurons of the
suprachiasmatic nucleus as chemically-coupled modified Goodwin oscillators, and
introduce non-negligible heterogeneity in the periods of all neurons in the
form of quenched noise. The system response to the light-dark cycle periodicity
is studied as a function of the interneuronal coupling strength, external
forcing amplitude and neuronal heterogeneity. Our results indicate that the
right amount of heterogeneity helps the extended system to respond globally in
a more coherent way to the external forcing. Our proposed mechanism for
neuronal synchronization under external periodic forcing is based on
heterogeneity-induced oscillators death, damped oscillators being more
entrainable by the external forcing than the self-oscillating neurons with
different periods.
