Geodesic
Stable hyperbolic limit cycles for a class of differential systems
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2021), pp. 49-60

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In this paper, we introduce an explicit expression of invariant algebraic curves for a class of polynomial differential systems, then we introduce an explicit expression of its first integral. Moreover, we determine sufficient 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{IVM_2021_9_a5,
     author = {S. E. Hamizi and R. Boukoucha},
     title = {Stable hyperbolic limit cycles for a class of differential systems},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {49--60},
     publisher = {mathdoc},
     number = {9},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_9_a5/}
}
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S. E. Hamizi; R. Boukoucha. Stable hyperbolic limit cycles for a class of differential systems. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2021), pp. 49-60. http://geodesic.mathdoc.fr/item/IVM_2021_9_a5/