{"paper":{"title":"Snakes and ladders in an inhomogeneous neural field model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"Daniele Avitabile, Helmut Schmidt","submitted_at":"2014-03-05T08:14:36Z","abstract_excerpt":"Continuous neural field models with inhomogeneous synaptic connectivities are known to support traveling fronts as well as stable bumps of localized activity. We analyze stationary localized structures in a neural field model with periodic modulation of the synaptic connectivity kernel and find that they are arranged in a snakes-and-ladders bifurcation structure. In the case of Heaviside firing rates, we construct analytically symmetric and asymmetric states and hence derive closed-form expressions for the corresponding bifurcation diagrams. We show that the ideas proposed by Beck and co-worke"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1037","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}