Exercise 186

1 Analyze the local stability of each of the following nonlinear systems:

(a) x' = ex - 1 (c) x' = 1 — ey y' = yex y' = 5 x — y

(b) x' = x + 2y (d) x' = x3 + 3x2y + y y' = x2 + y y' = x(l + y2)

2 Use Table 18.1 to determine the type of equilibrium a nonlinear system would have locally, given that:

(a) /t = 0

0 0

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