Pattern Formation in an Array of Oscillators with Electrical and Chemical Coupling | Zendy

Fatma Gürel Kazanci | Zendy; Bard Ermentrout | Zendy

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Pattern Formation in an Array of Oscillators with Electrical and Chemical Coupling

Author(s) -

Fatma Gürel Kazanci,

Bard Ermentrout

Publication year - 2007

Publication title -

siam journal on applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.954

H-Index - 99

eISSN - 1095-712X

pISSN - 0036-1399

DOI - 10.1137/060661041

Subject(s) - synchronizing , bifurcation , coupling (piping) , electrical synapses , physics , mechanics , phase (matter) , statistical physics , classical mechanics , mathematics , materials science , chemistry , nonlinear system , topology (electrical circuits) , quantum mechanics , gap junction , biochemistry , intracellular , combinatorics , metallurgy

Weak coupling theory is applied to a model for firing waves in the procerebral lobe of the slug. Inhibitory synapses and electrical synapses have different synchronizing properties. We show that, in concert, these two types of coupling can cause a bifurcation to a patterned state from synchrony which ultimately develops into traveling waves. Normal forms for the bifurcation are computed, and the results are compared to numerical simulations of the phase models.

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