{"paper":{"title":"Coherence transition in degenerate diffusion equations with mean field coupling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.AO","authors_text":"Khashayar Pakdaman, Xavier Pellegrin","submitted_at":"2012-02-29T12:04:41Z","abstract_excerpt":"We introduce non-linear diffusion in a classical diffusion advection model with non local aggregative coupling on the circle, that exhibits a transition from an uncoherent state to a coherent one when the coupling strength is increased. We show first that all solutions of the equation converge to the set of equilibria, second that the set of equilibria undergoes a bifurcation representing the transition to coherence when the coupling strength is increased. These two properties are similar to the situation with linear diffusion. Nevertheless nonlinear diffusion alters the transition scenari, wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6521","kind":"arxiv","version":1},"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"}