Chimeras as a way to model anatomical reentry in cardiac models

The FitzHugh-Nagumo (FHN) model is a two variable dynamical system that adequately describes many phenomena in excitable biological tissue. When used to model coupled oscillators in 2D space, solutions look like traveling waves, phase synchronization, or spiral waves. These solutions can be useful particularly when describing membrane potentials of cardiac tissue cells. Of interest are the dynamics of membrane potentials in tissue when there are unresponsive cells, causing waves to travel around and cause reentry leading to more deadly behavior like arrythmias and fibrillation. We consider chimera states, where there are spatial-temporal patterns of coupled oscillators that are made from two or more patterns. The appearance of chimeras is thought to require non-local coupling among oscillators and have exhibited regions of coordinated oscillations and uncoordinated oscillations. For past studies of chimera states in FHN, coupling exists among both the membrane potential variable and the relaxation variable, which is unphysical when comparing to a cardiac system. We present an extension to a FHN system with purely local coupling that models waves and unresponsive cells and explore the rich dynamics that result.