{"paper":{"title":"Period-halving Bifurcation of a Neuronal Recurrence Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","nlin.CD"],"primary_cat":"cs.NE","authors_text":"Ren\\'e Ndoundam","submitted_at":"2011-10-17T07:10:26Z","abstract_excerpt":"We study the sequences generated by neuronal recurrence equations of the form $x(n) = {\\bf 1}[\\sum_{j=1}^{h} a_{j} x(n-j)- \\theta]$. From a neuronal recurrence equation of memory size $h$ which describes a cycle of length $\\rho(m) \\times lcm(p_0, p_1,..., p_{-1+\\rho(m)})$, we construct a set of $\\rho(m)$ neuronal recurrence equations whose dynamics describe respectively the transient of length $O(\\rho(m) \\times lcm(p_0, ..., p_{d}))$ and the cycle of length $O(\\rho(m) \\times lcm(p_{d+1}, ..., p_{-1+\\rho(m)}))$ if $0 \\leq d \\leq -2+\\rho(m)$ and 1 if $d=\\rho(m)-1$.\n  This result shows the expone"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3586","kind":"arxiv","version":3},"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"}