Instability of the Standing Pulse in Skew-Gradient Systems and Its Application to FitzHugh-Nagumo Type Systems

In this paper, we use the Maslov index to obtain a lower bound on the number of unstable eigenvalues associated with standing pulse solutions in skew-gradient systems. Based on this, we establish an instability criterion for the standing pulse. As an application, the results are applied to FitzHugh-Nagumo type systems, in which the activator and inhibitor reaction terms exhibit inherent nonlinear structures.