Question

Denote the owl and wood rat populations at time k by where k is in months, O is the number of owls, and Rx is the number of rats (in thousands).Suppose Ok and Rk satisfy the equations below. Determine the evolution of the dynamical system. (Give a formula forX) As time passes, what happens to the sizes of the awl and wood rat populations? The system tends toward what is sometimes called an unstable equilibrium. What might happen to the system if some aspect of the model (such as birth rates or the predation rate) were to change slightly? Rk1-042)0+(1.3)R As time passes, what happens to the sizes of the owl and wood rat populations? Select the correct choice below and fill in the answer boxes within your choice. Type whole numbers.) O A. The owl and wood rat populations grow at a rate of owl s) tothousand rats. O B. The owl and wood rat populations decline at a rate of owls) tothousand rats. OC. The owl and wood rat populations each stabilize in size. Eventually, the populations are in the approximate simplified ratio of owl s) to thousand rats. As currently described, the system tends toward equilibrium because one eigenvalue of the coefficient matrix A is characteristic equation would change s ghtly and the matrix A m ght not have ▼ as an eigen alue the eige value becomes s g and the other is VIf some aspect of the model were to change slightly, the / arger than that value the two o ulations If the eigenvalue becomes slightly less than that value, both populations will

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