Global Phase Portraits of Kukles Differential Systems with Homogeneous Polynomial Nonlinearities of Degree 6 Having a Center and Their Small Limit Cycles
| Autor: | Maurício Fronza da Silva, Jaume Llibre |
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| Rok vydání: | 2016 |
| Předmět: |
Polynomial
Class (set theory) Degree (graph theory) Phase portrait Computer Science::Information Retrieval Applied Mathematics Poincaré disk model 010102 general mathematics Mathematical analysis Astrophysics::Instrumentation and Methods for Astrophysics Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) 010103 numerical & computational mathematics Center (group theory) 01 natural sciences symbols.namesake Modeling and Simulation Homogeneous polynomial symbols Computer Science::General Literature Limit (mathematics) 0101 mathematics Engineering (miscellaneous) Mathematics |
| Zdroj: | International Journal of Bifurcation and Chaos. 26:1650044 |
| ISSN: | 1793-6551 0218-1274 |
| DOI: | 10.1142/s0218127416500449 |
| Popis: | We provide the nine topological global phase portraits in the Poincaré disk of the family of the centers of Kukles polynomial differential systems of the form [Formula: see text] [Formula: see text] where [Formula: see text] and [Formula: see text] are real parameters satisfying [Formula: see text] Using averaging theory up to sixth order we determine the number of limit cycles which bifurcate from the origin when we perturb this system first inside the class of all homogeneous polynomial differential systems of degree [Formula: see text] and second inside the class of all polynomial differential systems of degree [Formula: see text] |
| Databáze: | OpenAIRE |
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