Chimera States with Local Coupling: the 5^th Order FitzHugh-Nagumo Model

The FitzHugh-Nagumo model is a simple, two variable dynamical system that adequately describes many phenomena in excitable biological systems, such as firing neurons. The excitability is modeled via cubic terms added to the otherwise linear differential equations, resulting in either a stable fixed point or a stable limit cycle which describes synchronized oscillating cells. However, chimera states in which stable fixed-point and limit-cycle regions coexist are not described within this model, even though they are observed in the heart and the brain. By adding a 5^th order term in the membrane potential to this 3^rd order system, we can recover chimeras, dependent on only initial conditions of the cells. Chimeras have previously been shown in systems with non-local coupling. We present this new system with purely local coupling. We study the dynamics of these chimeras in a few situations: in 1-dimensional cables and rings with two different simultaneous dynamics and in 2-dimensional grids representing tissues, with four different simultaneous dynamics. We want to investigate if the introduction of this 5^th order term is able to predict new phenomena in biological systems.