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This article communicates results on regular depolarization cascades inperiodically-kicked feedforward chains of excitable two-dimensionalFitzHugh-Nagumo systems driven by sufficiently strong excitatory forcing at thefront node. The study documents a parameter exploration by way of changes tothe forcing period, upon which the dynamics undergoes a transition from simpledepolarization to more complex behavior, including the emergence of mixed-modeoscillations. Both rigorous studies and careful numerical observations arepresented. In particular, we provide rigorous proofs for existence andstability of periodic traveling waves of depolarization, as well as theexistence and propagation of a simple mixed-mode oscillation that featuresdepolarization and refraction in alternating fashion. Detailed numericalinvestigation reveals a mechanism for the emergence of complex mixed-modeoscillations featuring a potentially high number of large amplitude voltagespikes interspersed by an occasional small amplitude reset that fails to crossthreshold. Further careful numerical investigation provides insights into thepropagation of this complex phenomenology in the downstream, where we see aneffective filtration property of the network; the latter amounts to asuccessive reduction in the complexity of mixed-mode oscillations down thechain.

Periodically kicked feedforward chains of simple excitable FitzHugh-Nagumo neurons