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- W3018396540 abstract "Abstract We apply the averaging theory of first and second order for studying the limit cycles of generalized polynomial Linard systems of the form <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mover> <m:mi>x</m:mi> <m:mo>˙</m:mo> </m:mover> <m:mo>=</m:mo> <m:mi>y</m:mi> <m:mo>-</m:mo> <m:mn>1</m:mn> <m:mrow> <m:mo>(</m:mo> <m:mi>x</m:mi> <m:mo>)</m:mo> </m:mrow> <m:mi>y</m:mi> <m:mo>,</m:mo> <m:mi> </m:mi> <m:mi> </m:mi> <m:mover> <m:mi>y</m:mi> <m:mo>˙</m:mo> </m:mover> <m:mo>=</m:mo> <m:mo>-</m:mo> <m:mi>x</m:mi> <m:mo>-</m:mo> <m:mi>f</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mi>x</m:mi> <m:mo>)</m:mo> </m:mrow> <m:mo>-</m:mo> <m:mi>g</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mi>x</m:mi> <m:mo>)</m:mo> </m:mrow> <m:mi>y</m:mi> <m:mo>-</m:mo> <m:mi>h</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mi>x</m:mi> <m:mo>)</m:mo> </m:mrow> <m:msup> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mn>2</m:mn> </m:msup> <m:mo>,</m:mo> </m:mrow> </m:math> dot x = y - 1left( x right)y,,,dot y = - x - fleft( x right) - gleft( x right)y - hleft( x right){y^2}, where l ( x ) = ∊l 1 ( x ) + ∊ 2 l 2 ( x ), f ( x ) = ∊ f 1 ( x ) + ∊ 2 f 2 ( x ), g ( x ) = ∊g 1 ( x ) + ∊ 2 g 2 ( x ) and h ( x ) = ∊h 1 ( x ) + ∊ 2 h 2 ( x ) where l k ( x ) has degree m and f k ( x ), g k ( x ) and h k ( x ) have degree n for each k = 1, 2, and ∊ is a small parameter." @default.
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- W3018396540 date "2020-05-29" @default.
- W3018396540 modified "2023-10-18" @default.
- W3018396540 title "Limit cycles of Liénard polynomial systems type by averaging method" @default.
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- W3018396540 doi "https://doi.org/10.2478/mjpaa-2020-0001" @default.
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