{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","description":"This cluster of papers focuses on the study of bifurcations in planar polynomial systems, particularly emphasizing piecewise linear structures, limit cycles, Hopf bifurcations, discontinuous systems, nilpotent singularities, Darboux integrability, and Abelian integrals.","keywords":[{"id":"https://openalex.org/keywords/limit-cycles","display_name":"limit cycles","score":0.336},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"bifurcation theory","score":0.3346},{"id":"https://openalex.org/keywords/normal-forms","display_name":"normal forms","score":0.2023},{"id":"https://openalex.org/keywords/polynomial-vector-fields","display_name":"polynomial vector fields","score":0.7368},{"id":"https://openalex.org/keywords/planar-dynamical-systems","display_name":"planar dynamical systems","score":0.4957},{"id":"https://openalex.org/keywords/homoclinic-orbits","display_name":"homoclinic orbits","score":0.2652},{"id":"https://openalex.org/keywords/planar-vector-fields","display_name":"planar vector fields","score":0.8156},{"id":"https://openalex.org/keywords/bifurcation-of-limit-cycles","display_name":"bifurcation of limit cycles","score":0.9305},{"id":"https://openalex.org/keywords/qualitative-theory-of-differential-equations","display_name":"qualitative theory of differential equations","score":0.4108},{"id":"https://openalex.org/keywords/polynomial-differential-systems","display_name":"polynomial differential systems","score":0.9328},{"id":"https://openalex.org/keywords/piecewise-smooth-systems","display_name":"piecewise-smooth systems","score":0.5505},{"id":"https://openalex.org/keywords/lienard-systems","display_name":"Li\u00e9nard systems","score":0.8249},{"id":"https://openalex.org/keywords/central-configurations","display_name":"central configurations","score":0.7484},{"id":"https://openalex.org/keywords/homoclinic-bifurcation","display_name":"homoclinic bifurcation","score":0.2973},{"id":"https://openalex.org/keywords/quadratic-systems","display_name":"quadratic systems","score":0.65},{"id":"https://openalex.org/keywords/center-manifold","display_name":"center manifold","score":0.257},{"id":"https://openalex.org/keywords/center-focus-problem","display_name":"center-focus problem","score":0.9424},{"id":"https://openalex.org/keywords/planar-polynomial-differential-systems","display_name":"planar polynomial differential systems","score":0.9736},{"id":"https://openalex.org/keywords/lienard-equation","display_name":"Li\u00e9nard equation","score":0.6032},{"id":"https://openalex.org/keywords/melnikov-function","display_name":"Melnikov function","score":0.504},{"id":"https://openalex.org/keywords/codimension-2-bifurcation","display_name":"codimension-two bifurcation","score":0.3203},{"id":"https://openalex.org/keywords/planar-differential-equations","display_name":"planar differential equations","score":0.8889},{"id":"https://openalex.org/keywords/stability-of-periodic-solutions","display_name":"stability of periodic solutions","score":0.2579},{"id":"https://openalex.org/keywords/discontinuous-dynamical-systems","display_name":"discontinuous dynamical systems","score":0.3985},{"id":"https://openalex.org/keywords/planar-polynomial-vector-fields","display_name":"planar polynomial vector fields","score":0.9587}],"legacy_keywords":"Bifurcations; Planar Systems; Piecewise Linear; Limit Cycles; Polynomial Vector Fields; Hopf Bifurcation; Discontinuous Systems; Nilpotent Singularity; Darboux Integrability; Abelian Integrals","ids":{"openalex":"https://openalex.org/T12396","wikipedia":"https://en.wikipedia.org/wiki/Bifurcation_theory"},"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"},"siblings":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory"},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models"},{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology"},{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory"},{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications"},{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis"},{"id":"https://openalex.org/T11822","display_name":"Analytic and geometric function theory"},{"id":"https://openalex.org/T12351","display_name":"Geometry and complex manifolds"},{"id":"https://openalex.org/T12417","display_name":"Morphological variations and asymmetry"},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications"}],"works_count":56952,"cited_by_count":588161,"works_api_url":"https://api.openalex.org/works?filter=topics.id:T12396","updated_date":"2026-10-20T03:01:21","created_date":"2024-01-23T15:27:14"}