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• W4367050106 abstract "We investigate the singularly perturbed monotone systems with respect to cones of rank <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=2> <mml:semantics> <mml:mn>2</mml:mn> <mml:annotation encoding=application/x-tex>2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and obtain the so called Generic Poincaré-Bendixson theorem for such perturbed systems, that is, for a bounded positively invariant set, there exists an open and dense subset <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper P> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>P</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {P}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such that for each <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=z element-of script upper P> <mml:semantics> <mml:mrow> <mml:mi>z</mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>P</mml:mi> </mml:mrow> </mml:mrow> <mml:annotation encoding=application/x-tex>zin mathcal {P}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, the <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=omega> <mml:semantics> <mml:mi>ω<!-- ω --></mml:mi> <mml:annotation encoding=application/x-tex>omega</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-limit set <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=omega left-parenthesis z right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>ω<!-- ω --></mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>z</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>omega (z)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> that contains no equilibrium points is a closed orbit." @default.
• W4367050106 created "2023-04-27" @default.
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• W4367050106 date "2023-07-21" @default.
• W4367050106 modified "2023-09-27" @default.
• W4367050106 title "Generic Poincaré-Bendixson theorem for singularly perturbed monotone systems with respect to cones of rank-2" @default.
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