Limit Cycles and the Poincaré-Bendixson Theorem 1. Show that the nonlinear two dimensional systenm z'(t) x(t) + y(t)-エ(t)(z"(t)-r(t)), has the single critical point (0,0). Hint: show that the only solution to is y 0, by first changing to polar coordinates and then proving that-ea+v' = 0 is the only solution, i.e that there are no solutions (r.0) with r>0
Limit Cycles and the Poincaré-Bendixson Theorem 1. Show that the nonlinear two dimensional systenm z'(t) x(t) + y(t)-エ(t)(z"(t)-r(t)), has the single critical point (0,0). Hint: show that the only solution to is y 0, by first changing to polar coordinates and then proving that-ea+v' = 0 is the only solution, i.e that there are no solutions (r.0) with r>0
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 70EQ
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