  We study numerically the spatiotemporal dynamics in a ring network of
nonlocally coupled nonlinear oscillators, each represented by a two-dimensional
discrete-time model of the classical van der Pol oscillator. It is shown that
the discretized oscillator exhibits a richer behavior, combining the
peculiarities of both the original system and its own dynamics. Moreover, a
large variety of spatiotemporal structures is observed in the network of
discrete van der Pol oscillators when the discretization parameter and the
coupling strength are varied. Regimes such as the coexistence of multichimera
state/traveling wave and solitary state are revealed for the first time and are
studied in detail. It is established that the majority of the observed
chimera/solitary states, including the newly found ones, are transient towards
the purely traveling wave mode. The peculiarities of the transition process and
the lifetime (transient duration) of the chimera structures and the solitary
state are analyzed depending on the system parameters, the observation time,
initial conditions, and the influence of external noise.
