Different synchronization characteristics of distinct types of traveling waves in a model of active medium with periodic boundary conditions

• The phenomenon of multistability of traveling waves is observed for all regimes.
• The dispersion curves of different regimes of the medium have a different character.
• The synchronization effects in different regimes show a qualitative difference.

The model of a one-dimensional active medium, which cells are the FitzHugh–Nagumo oscillators, is studied for periodical boundary conditions. The medium possesses three different regimes in dependence on the parameter values. The regimes correspond to the self-sustained oscillations, excitable dynamics or bistability of the medium cells. Periodic boundary conditions provide the existence of traveling wave modes in all mentioned cases without any deterministic or stochastic excitation. The spatial waveforms and the character of oscillations in time can be similar in the different cases, but the properties of wave modes depend considerably on the medium regime. So, the dispersion characteristics and the synchronization phenomena are essentially different for bistable and excitable media on the one hand, and for the self-sustained oscillatory medium on the other hand. The local and distributed periodic influence on the medium are studied. The phenomenon of the traveling wave frequency locking is observed for all three regimes of the active medium. The comparison of synchronization effects in self-oscillatory, excitable and bistable regimes of the active medium is carried out.