Kopell, Nancy; Somers, David Anti-phase solutions in relaxation oscillators coupled through excitatory interactions. (English) Zbl 0828.92005 J. Math. Biol. 33, No. 3, 261-280 (1995). Summary: Relaxation oscillators interacting via models of excitatory chemical synapses with sharp thresholds can have stable anti-phase as well as in- phase solutions. The mechanism for anti-phase demonstrated in this paper relies on the fact that, in a large class of neural models, excitatory input slows down the receiving oscillator over a portion of its trajectory. We analyze the effect of this “virtual delay” in an abstract model, and then show that the hypotheses of that model hold for widely used descriptions of bursting neurons. Cited in 1 ReviewCited in 25 Documents MSC: 92C20 Neural biology 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations Keywords:relaxation oscillators; virtual delay; neural oscillator; pulse coupling; bistability; synaptic coupling; van der Pol oscillator; excitatory chemical synapses; thresholds; anti-phase; excitatory input; bursting neurons PDFBibTeX XMLCite \textit{N. Kopell} and \textit{D. Somers}, J. Math. Biol. 33, No. 3, 261--280 (1995; Zbl 0828.92005) Full Text: DOI