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Unformatted text preview: 2. Consider the competing species system ˙ x = x ± 141 2 xy ² , ˙ y = y ± 161 2 yx ² Find all the ﬁxed points and study their linear stability. Assuming x ( t ) ≥ 0 and y ( t ) ≥ 0, put the information together in a phase portrait. Discuss the longterm evolution of the two species based on these results. 3. Using the identities θ = tan1 ± y x ² , r 2 = x 2 + y 2 show that ˙ θ = x ˙ yy ˙ x r 2...
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This note was uploaded on 02/20/2011 for the course MATH 503 taught by Professor Schleiniger,g during the Fall '08 term at University of Delaware.
 Fall '08
 Schleiniger,G
 Math, Calculus

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