Bifurcations of the Riccati quadratic polynomial differential systems
| Autor: | Bruno D. Lopes, Jaume Llibre, Paulo Ricardo da Silva |
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| Přispěvatelé: | Univ Autonoma Barcelona, Universidade Estadual de Campinas (UNICAMP), Universidade Estadual Paulista (Unesp) |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Phase portrait Poincaré compactification 010308 nuclear & particles physics Computer Science::Information Retrieval Applied Mathematics 010102 general mathematics Astrophysics::Instrumentation and Methods for Astrophysics Topological equivalence Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) Quadratic function Riccati system Differential systems 01 natural sciences Modeling and Simulation 0103 physical sciences Computer Science::General Literature Bifurcation 0101 mathematics Engineering (miscellaneous) Dynamics at infinity Poincare compactification Mathematics |
| Zdroj: | Dipòsit Digital de Documents de la UAB Universitat Autònoma de Barcelona Web of Science Repositório Institucional da UNESP Universidade Estadual Paulista (UNESP) instacron:UNESP |
| Popis: | Made available in DSpace on 2021-06-25T15:06:27Z (GMT). No. of bitstreams: 0 Previous issue date: 2021-05-01 Ministerio de Economia, Industria y Competitividad, Agencia Estatal de Investigacion grant Agencia de Gestio d'Ajuts Universitaris i de Recerca grant H2020 European Research Council grant Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) In this paper, we characterize the global phase portrait of the Riccati quadratic polynomial differential system (x) over dot = alpha(2) (x), (y) over dot = ky(2) + beta(1)(x)y + -gamma(2)(x), with (x,y) is an element of R-2, gamma(2)(x) nonzero (otherwise the system is a Bernoulli differential system), k not equal 0 (otherwise the system is a Lienard differential system), beta(1)(x) a polynomial of degree at most 1, alpha(2)(x) and -gamma(2)(x) polynomials of degree at most 2, and the maximum of the degrees of alpha(2)(x) and ky(2) + beta(1)(x)y + gamma(2)(x) is 2. We give the complete description of the phase portraits in the Poincare disk (i.e. in the compactification of R-2 adding the circle S-1 of the infinity) modulo topological equivalence. Univ Autonoma Barcelona, Dept Matemat, Barcelona 08193, Catalonia, Spain Univ Estadual Campinas, IMECC, BR-13081970 Campinas, S Paulo, Brazil IBILCE Univ Estadual Paulista, Dept Matemat, Rua C Colombo 2265, BR-15054000 Sjr Preto, S Paulo, Brazil IBILCE Univ Estadual Paulista, Dept Matemat, Rua C Colombo 2265, BR-15054000 Sjr Preto, S Paulo, Brazil Ministerio de Economia, Industria y Competitividad, Agencia Estatal de Investigacion grant: MTM201677278-P Agencia de Gestio d'Ajuts Universitaris i de Recerca grant: 2017SGR1617 H2020 European Research Council grant: MSCA-RISE-2017-777911 : FP7-PEOPLE-2012-IRSES-316338 |
| Databáze: | OpenAIRE |
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