On Global Asymptotic Stability of Second Order Nonlinear Differential Systems |
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Authors: | Yan Ping Jiang Jifa |
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Institution: | 1. Department of Mathematics , University of Turku , Turku, FIN-20014, Finland;2. Department of Mathematics , University of Science and Technology of China , Hefei, People's Republic of China |
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Abstract: | This paper investigates the global asymptotic stability of the autonomous planar systems $ \dot {x} = p_2(y)q_2(x)y $ , $ \dot {y} = p_3(y)q_3(x)x + p_3(y)q_4(x)y $ and $ \dot {x} = f_1(x) + h_2(x)y $ , $ \dot {y} = f_3(x) + h_4(x)y $ , under the assumption that all functions involved in the equations are continuous and that the origin is a unique equilibrium. We present necessary and sufficient conditions for the origin to be globally asymptotically stable. |
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Keywords: | Second Order Differential System Global Asymptotic Stability Filippov Transformation |
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