The accumulation of eigenvalues in a stability problem
Sufficient criteria for instability of pulses in reaction-diffusion systems, formed by gluing together a front and a back at a PDE-unstable equilibrium, are given. The pulses exhibit a long intermediate plateau between front and back. In the travelling-wave ODE, the pulses are created as homoclinic orbits in a codimension-two heteroclinic loop bifurcation, sometimes referred to as a \(T\)-point. The PDE-instability is caused by an absolute instability of the unstable state at the plateau. As the length of the plateau tends to infinity, infinitely many unstable eigenvalues are shown to accumulate at a certain spectral value in the unstable complex plain.
sufficient criteria for instability of pulses
homoclinic orbits in a codimension-two heteroclinic loop bifurcation
scientific article; zbMATH DE number 1474681