Geodesic
Maximum number of limit cycles for generalized Liénard polynomial differential systems
Mathematica Bohemica, Tome 146 (2021) no. 2, pp. 151-165
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We consider limit cycles of a class of polynomial differential systems of the form $$ \begin {cases} \dot {x}=y, \\ \dot {y}=-x-\varepsilon (g_{21}( x) y^{2\alpha +1} +f_{21}(x) y^{2\beta })-\varepsilon ^{2}(g_{22}( x) y^{2\alpha +1}+f_{22}( x) y^{2\beta }), \end {cases} $$ where $\beta $ and $\alpha $ are positive integers, $g_{2j}$ and $f_{2j}$ have degree $m$ and $n$, respectively, for each $j=1,2$, and $\varepsilon $ is a small parameter. We obtain the maximum number of limit cycles that bifurcate from the periodic orbits of the linear center $\dot {x}=y$, $\dot {y}=-x$ using the averaging theory of first and second order.
We consider limit cycles of a class of polynomial differential systems of the form $$ \begin {cases} \dot {x}=y, \\ \dot {y}=-x-\varepsilon (g_{21}( x) y^{2\alpha +1} +f_{21}(x) y^{2\beta })-\varepsilon ^{2}(g_{22}( x) y^{2\alpha +1}+f_{22}( x) y^{2\beta }), \end {cases} $$ where $\beta $ and $\alpha $ are positive integers, $g_{2j}$ and $f_{2j}$ have degree $m$ and $n$, respectively, for each $j=1,2$, and $\varepsilon $ is a small parameter. We obtain the maximum number of limit cycles that bifurcate from the periodic orbits of the linear center $\dot {x}=y$, $\dot {y}=-x$ using the averaging theory of first and second order.
DOI : 10.21136/MB.2020.0134-18
Classification : 34C07, 34C23, 37G15
Keywords: polynomial differential system; limit cycle; averaging theory 
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Berbache, Aziza; Bendjeddou, Ahmed; Benadouane, Sabah. Maximum number of limit cycles for generalized Liénard polynomial differential systems. Mathematica Bohemica, Tome 146 (2021) no. 2, pp. 151-165. doi: 10.21136/MB.2020.0134-18

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