  Coupled dynamical systems in ecology are known to respond to the seasonal
forcing of their parameters with multiple dynamical behaviours, ranging from
seasonal cycles to chaos. Seasonal forcing is predominantly modelled as a sine
wave but the transition between seasons is often more sudden. Some studies
mentioned the robustness of their results to the shape of the forcing signal,
without detailed analyses. Therefore, whether and how the shape of seasonal
forcing affects the dynamics of coupled dynamical systems remains unclear,
while abrupt seasonal transitions are widespread in ecological systems. To
provide some answers, we conduct a numerical analysis of the dynamical response
of predator--prey communities to the shape of the forcing signal by exploring
the joint effect of two features of seasonal forcing: the magnitude of the
signal, which is classically the only one studied, and the shape of the signal,
abrupt or sinusoidal. We consider both linear and saturating functional
responses, and focus on seasonal forcing of the predator's discovery rate,
which fluctuates with changing environmental conditions and prey's ability to
escape predation. Our numerical results highlight that a more abrupt seasonal
forcing mostly alters the magnitude of population fluctuations and triggers
period--doubling bifurcations, as well as the emergence of chaos, at lower
forcing strength than for sine waves. Controlling the variance of the forcing
signal mitigates this trend but does not fully suppress it, which suggests that
the variance is not the only feature of the shape of seasonal forcing that acts
on community dynamics. Although theoretical studies may predict correctly the
sequence of bifurcations using sine waves as a representation of seasonality,
there is a rationale for applied studies to implement as realistic seasonal
forcing as possible to make precise predictions of community dynamics.
