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Instability of the Standing Pulse in Skew-Gradient Systems and Its Application to FitzHugh-Nagumo Type Systems (2504.11211v1)
Published 15 Apr 2025 in math.AP and math.DS
Abstract: 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.
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