Geodesic
Limit cycles and phase portrait for a class of differential systems
Matematičeskie zametki SVFU, Tome 29 (2022) no. 2, pp. 72-81 Cet article a éte moissonné depuis la source Math-Net.Ru

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We introduce an explicit expression of invariant algebraic curves for a class of polynomial differential systems and an explicit expression for its first integral. Moreover, we determine suficient conditions for these systems to possess a limit cycle, which can be expressed by an explicit formula. Concrete examples exhibiting the applicability of our results are introduced.
Keywords: Hilbert 16th problem, dynamical system, limit cycle, invariant algebraic curve, first integral. 
@article{SVFU_2022_29_2_a5,
     author = {R. Boukoucha},
     title = {Limit cycles and phase portrait for a class of differential systems},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {72--81},
     year = {2022},
     volume = {29},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2022_29_2_a5/}
}
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R. Boukoucha. Limit cycles and phase portrait for a class of differential systems. Matematičeskie zametki SVFU, Tome 29 (2022) no. 2, pp. 72-81. http://geodesic.mathdoc.fr/item/SVFU_2022_29_2_a5/