dorsal/arxiv
View SchemaVariational calculation of the limit cycle and its frequency in a two-neuron model with delay
| Authors | Sebastian F. Brandt, Axel Pelster, Ralf Wessel |
|---|---|
| Categories | |
| ArXiv ID | physics/0603077 |
| URL | https://arxiv.org/abs/physics/0603077 |
| DOI | 10.1103/PhysRevE.74.036201 |
| Journal | Phys. Rev. E 74, 036201/1-14 (2006) |
Abstract
We consider a model system of two coupled Hopfield neurons, which is described by delay differential equations taking into account the finite signal propagation and processing times. When the delay exceeds a critical value, a limit cycle emerges via a supercritical Hopf bifurcation. First, we calculate its frequency and trajectory perturbatively by applying the Poincar\'e-Lindstedt method. Then, the perturbation series are resummed by means of the Shohat expansion in good agreement with numerical values. However, with increasing delay, the accuracy of the results from the Shohat expansion worsens. We thus apply variational perturbation theory (VPT) to the perturbation expansions to obtain more accurate results, which moreover hold even in the limit of large delays.
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"abstract": "We consider a model system of two coupled Hopfield neurons, which is\ndescribed by delay differential equations taking into account the finite signal\npropagation and processing times. When the delay exceeds a critical value, a\nlimit cycle emerges via a supercritical Hopf bifurcation. First, we calculate\nits frequency and trajectory perturbatively by applying the\nPoincar\\\u0027e-Lindstedt method. Then, the perturbation series are resummed by\nmeans of the Shohat expansion in good agreement with numerical values. However,\nwith increasing delay, the accuracy of the results from the Shohat expansion\nworsens. We thus apply variational perturbation theory (VPT) to the\nperturbation expansions to obtain more accurate results, which moreover hold\neven in the limit of large delays.",
"arxiv_id": "physics/0603077",
"authors": [
"Sebastian F. Brandt",
"Axel Pelster",
"Ralf Wessel"
],
"categories": [
"physics.bio-ph"
],
"doi": "10.1103/PhysRevE.74.036201",
"journal_ref": "Phys. Rev. E 74, 036201/1-14 (2006)",
"title": "Variational calculation of the limit cycle and its frequency in a two-neuron model with delay",
"url": "https://arxiv.org/abs/physics/0603077"
},
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