Itinerant chimeras in an adaptive network of pulse-coupled oscillators

Abstract: In a network of pulse-coupled oscillators with adaptive coupling, we a dynamical regime which we call an `itinerant chimera'. Similarly as in classical chimera states, the network splits into two domains, the coherent and the incoherent ones. The drastic difference is that the composition of the domains is volatile, i.e. the oscillators demonstrate spontaneous switching between the domains. This process can be seen as traveling of the oscillators from one domain to another, or as traveling of the chimera core across network. We explore the basic features of the itinerant chimeras, such as the mean and the variance of the core size, and the oscillators lifetime within the core. We also study the scaling behavior of the system and show that the observed regime is not a finite-size effect but a key feature of the collective dynamics which persists even in large networks.