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Download C - Maths, NUS
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Critical Point at (c/ï§, a/ï¡): Ellipses (4 of 7) Near the critical point (c/ï§, a/ï¡), we thus have dv ï§ 2a u ï½ï 2 ï ï¨ï§ 2 a u ï©du ï« ï¨ï¡ 2c v ï©dv ï½ 0 du ï¡ cv The solution to this separable equation is ï§ 2 a u 2 ï« ï¡ 2c v 2 ï½ k , k ï¾ 0 Thus the trajectories of the linear system are ellipses centered at the critical point (c/ï§, a/ï¡). Returning to the nonlinear system dx / dt ï½ xï¨a ï ï¡ y ï©, dy / dt ï½ yï¨ï c ï« ï§ xï© we have dy y ï¨ï c ï« ï§ x ï© ï½ dx xï¨a ï ï¡ y ï©
