2 citations · 3 across the 7 of their papers we have counts for
7 papers
Periodic travelling waves in the theta model for synaptically connected neurons
Guy Katriel
We study periodic travelling waves in the Theta model for a linear continuum of synaptically-interacting neurons. We prove that when the neurons are oscillatory, at least one perio…
Rotating waves in the Theta model for a ring of synaptically connected neurons
Guy Katriel
We study rotating waves in the Theta model for a ring of synaptically-interacting neurons. We prove that when the neurons are oscillatory, at least one rotating wave always exists.…
Existence of travelling waves in discrete sine-Gordon rings
Guy Katriel
We prove existence results for travelling waves in discrete, damped, dc-driven sine-Gordon equations with periodic boundary conditions.
Synchronization in model networks of class I neurons
Guy Katriel
We study a modification of the canonical model for networks of class I neurons, presented by Hoppensteadt and Izhikevich, in which the 'pulse' emitted by a neuron is smooth rather…
From Rolle's theorem to the Sturm-Hurwitz theorem
Guy Katriel
We present a proof of the Sturm-Hurwitz theorem, using basic calculus.
Stability of synchronized oscillations in networks of phase-oscillators
Guy Katriel
We derive simple conditions for the stability or instability of the synchronized oscillation of a class of networks of coupled phase-oscillators, which includes many of the systems…