{"paper":{"title":"Phase Space Formulation of Population Dynamics in Ecology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"q-bio.PE","authors_text":"Jesus Martinez-Linares","submitted_at":"2013-04-08T19:23:20Z","abstract_excerpt":"A phase space theory for population dynamics in Ecology is presented. This theory applies for a certain class of dynamical systems, that will be called M-systems, for which a conserved quantity, the M-function, can be defined in phase space. This M-function is the generator of time displacements and contains all the dynamical information of the system. In this sense the M-function plays the role of the hamiltonian function for mechanical systems. In analogy with Hamilton theory we derive equations of motion as derivatives over the resource function in phase space. A M-bracket is defined which "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2324","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"}