dorsal/arxiv
View SchemaSynchronization in a neuronal feedback loop through asymmetric temporal delays
| Authors | Sebastian F. Brandt, Axel Pelster, Ralf Wessel |
|---|---|
| Categories | |
| ArXiv ID | physics/0701225 |
| URL | https://arxiv.org/abs/physics/0701225 |
| DOI | 10.1209/0295-5075/79/38001 |
| Journal | EPL 79, 38001 (2007) |
Abstract
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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"abstract": "We consider the effect of asymmetric temporal delays in a system of two\ncoupled Hopfield neurons. For couplings of opposite signs, a limit cycle\nemerges via a supercritical Hopf bifurcation when the sum of the delays reaches\na critical value. We show that the angular frequency of the limit cycle is\nindependent of an asymmetry in the delays. However, the delay asymmetry\ndetermines the phase difference between the periodic activities of the two\ncomponents. Specifically, when the connection with negative coupling has a\ndelay much larger than the delay for the positive coupling, the system\napproaches in-phase synchrony between the two components. Employing variational\nperturbation theory (VPT), we achieve an approximate analytical evaluation of\nthe phase shift, in good agreement with numerical results.",
"arxiv_id": "physics/0701225",
"authors": [
"Sebastian F. Brandt",
"Axel Pelster",
"Ralf Wessel"
],
"categories": [
"physics.bio-ph"
],
"doi": "10.1209/0295-5075/79/38001",
"journal_ref": "EPL 79, 38001 (2007)",
"title": "Synchronization in a neuronal feedback loop through asymmetric temporal delays",
"url": "https://arxiv.org/abs/physics/0701225"
},
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