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H.J.Hupkes, D.E. Pelinovsky, and B. Sandstede

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Propagation failure in the discrete Nagumo equation

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Proceedings of the AMS, 139, 3537–3551 (2011)

**Abstract:**

We address the classical problem of propagation failure for
monotonic fronts of the discrete Nagumo equation.
For a special class of nonlinearities that support unpinned
"translationally invariant" stationary monotonic
fronts, we prove that propagation failure cannot occur. Properties
of travelling fronts in the discrete Nagumo
equation with such special nonlinear functions appear to be
similar to those in the continuous Nagumo
equation.

**Keywords**:

lattice differential equation, propagation failure, discrete kink, normally hyperbolic invariant
manifold