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- W2469734838 abstract "This paper investigates Lotka-Volterra system under a small perturbation<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:msub><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mi>μ</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mn mathvariant=normal>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant=normal>2</mml:mn></mml:mrow></mml:msub><mml:mi>u</mml:mi><mml:mo>-</mml:mo><mml:mi>v</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mi>v</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant=normal>ϵ</mml:mi><mml:mi>f</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi mathvariant=normal>ϵ</mml:mi><mml:mo>,</mml:mo><mml:mi>v</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>u</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mo stretchy=false>)</mml:mo></mml:math>,<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:msub><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mo stretchy=false>(</mml:mo><mml:mn mathvariant=normal>1</mml:mn><mml:mo>-</mml:mo><mml:mi>u</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant=normal>1</mml:mn></mml:mrow></mml:msub><mml:mi>v</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mi>u</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant=normal>ϵ</mml:mi><mml:mi>g</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi mathvariant=normal>ϵ</mml:mi><mml:mo>,</mml:mo><mml:mi>v</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>u</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mo stretchy=false>)</mml:mo></mml:math>. By the Fourier series expansion technique method, the fixed point theorem, the perturbation theorem, and the reversibility, we prove that near<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mi>μ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=normal>0</mml:mn></mml:math>the system has a generalized homoclinic solution exponentially approaching a periodic solution." @default.
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- W2469734838 date "2016-01-01" @default.
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- W2469734838 title "Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation" @default.
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- W2469734838 doi "https://doi.org/10.1155/2016/8075381" @default.
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