Consider this nonlinear dynamical system da = 2x - x² - xy, dt dy = xy - Y dt a) Find the equilibrium points. b) Determine the nullclines of the system and sketch the directional field in the region x ≥ 0, y ≥ 0. c) Analyze the stability of the equilibrium point in which both species co-exist using the result above. d) Use the Jacobian matrix method to confirm the result of the analysis in (c) above.

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