Synchronization in a neuronal feedback loop through asymmetric temporal delays

Details Synchronization in a neuronal feedback loop through asymmetric temporal delays Synchronization in a neuronal feedback loop through asymmetric temporal delays

2007-01-19

arxiv.org/abs/physics/0701225v2

EPL 79, 38001 (2007)

Physics

Biological Physics

5 pages, 4 figures

Scientific paper

10.1209/0295-5075/79/38001

We consider the effect of asymmetric temporal delays in a system of two coupled Hopfield neurons. For couplings of opposite signs, a limit cycle emerges via a supercritical Hopf bifurcation when the sum of the delays reaches a critical value. We show that the angular frequency of the limit cycle is independent of an asymmetry in the delays. However, the delay asymmetry determines the phase difference between the periodic activities of the two components. Specifically, when the connection with negative coupling has a delay much larger than the delay for the positive coupling, the system approaches in-phase synchrony between the two components. Employing variational perturbation theory (VPT), we achieve an approximate analytical evaluation of the phase shift, in good agreement with numerical results.

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