  In the present work we reconsider the evolutionary game theoretic models by
Antoci et al. (2016, 2018) describing the dynamic outcomes arising from the
interactions between patients and physicians, whose behavior is subject to
clinical and legal risks. In particular, Antoci et al. (2016) analyzed the case
of positive defensive medicine, while Antoci et al. (2018) dealt with the case
of negative defensive medicine. We show that, when the models admit a
nonisochronous center, it is possible to prove the existence of chaotic
dynamics for the Poincar\'e map associated with those systems via the method of
Linked Twist Maps (LTMs). To such aim we exploit in both frameworks, using a
similar rationale, the periodic dependence on time of a model parameter
influencing the position of the center and describing some risk associated with
certain medical interventions, whose seasonal variation is empirically
grounded. We also provide the ecological interpretation of the same model,
proposed by Harvie et al. (2007) and connected with intraspecific competition
and environmental carrying capacity in predator-prey settings. In this case, it
is sensible to assume a seasonal variation both for the carrying capacities and
for the intrinsic growth rates of the two populations. Although such parameters
influence the shape of the orbits, but do not affect the center position, we
show that it is still possible to prove the existence of chaotic dynamics for
the associated Poincar\'e map via the LTMs technique dealing with a different
geometrical configuration for orbits in the phase plane.
