  Cardiac muscle cells can exhibit complex patterns including irregular
behaviour such as chaos or (chaotic) early afterdepolarisations (EADs), which
can lead to sudden cardiac death. Suitable mathematical models and their
analysis help to predict the occurrence of such phenomena and to decode their
mechanisms. The focus of this paper is the investigation of dynamics of cardiac
muscle cells described by systems of ordinary differential equations. This is
generically performed by studying a Purkinje cell model and a modified
ventricular cell model. We find chaotic dynamics with respect to the leak
current in the Purkinje cell model, and EADs and chaos with respect to a
reduced fast potassium current and an enhanced calcium current in the
ventricular cell model -- features that have been experimentally observed and
are known to exist in some models, but are new to the models under present
consideration. We also investigate the related monodomain models of both
systems to study synchronisation and the behaviour of the cells on macro-scale
in connection with the discovered features. The models show qualitatively the
same behaviour to what has been experimentally observed. However, for certain
parameter settings the dynamics occur within a non-physiological range.
