On Global Asymptotic Stability of Second Order Nonlinear Differential Systems
On Global Asymptotic Stability of Second Order Nonlinear Differential Systems
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DOI：
10.1080/0003681021000004375
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发表时间：
2002-01
影响因子：
1.1
通讯作者：
Yan Ping;Jiang Jifa
中科院分区：
文献类型：
--
作者：
Yan Ping;Jiang Jifa
本文研究了平面自治系统$ \dot {x} = p2（y）q2（x）y $，$ \dot {y} = p3（y）q3（x）x + p3（y）q4（x）y $和$ \dot {x} = f1（x）+h2（x）y $，$ \dot {y} = f3（x）+h4（x）y $的全局渐近稳定性，假设方程中的所有函数都是连续的，并且原点是唯一的平衡点。给出了原点全局渐近稳定的充分必要条件。
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.