Consider the system of ordinary differential equations

(a) Confirm that (x,y) = (0,0), (1,−1), and (−1,1) are steady states of this system.

(b) What is the 2 × 2 steady state Jacobian for this system in terms of x and y?

(c) Determine the stability and the classification (node, spiral, saddle point, center, or unknown) for each of the steady states in part (a).

Transcribed Image Text:

X-X₂x = zx + ax= dt dy dt dx