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

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.