Consider the following nonlinear predator-prey model: 6y₁ - 2y - y192, where dy₁ dt dy2 dt where y₁ (t) is the population of the prey species, and y2(t) is the population of the predator species. We can write this in vector form as y' = F(y), = y1y2 - 2y2, F(y) = - ( 1 (m. 12)) - (61 = (112). (a) Find the steady states of this system, i.e. the vectors (31,32) so that F(₁,32): (0,0). Hint: there are three steady states. (b) Calculate the total derivative DF(₁,32) = 6y₁-2y-9132 9192-2y2 (əfi əfi дуı дуг მ2 მ2 dy dy₂/ as a function of y₁ and y2. (c) For each steady state (y1, 32) from (a), find the eigenvalues of DF (y1, 92) and classify the steady state as stable or unstable.

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