MATH 616-010 Modeling in Applied Mathematics Prof. D. A. Edwards Sept. 13, 2018 Liapunov Functions For the case where ˙ x = -y - x 3 ˙ y = x - y 3 (1) we found that a Liapunov function was given by V = x 2 + y 2 , and that the origin is stable. -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 -0.4 -0.3 -0.2 -0.1 0.1 0.2 0.3 0.4 Phase plane of (1). Note the slow approach to the origin. Copyright ©2018 D. A. Edwards All Rights Reserved