Study Questions for Final

Which of the following sets of equations is non-linear?

(a)

n1[t+1] = a n1[t] + b n2[t]

n2[t+1] = c n1[t] / n2[t]

(b)
n1[t+1] = a n1[t] + b n2[t] - c n2[t]

n2[t+1] = d n1[t] + e n2[t] - f n2[t]

(c)
n1[t+1] = a n2[t]

n2[t+1] = b n1[t]

(d)
n1[t+1] = a n1[t] + b n1[t] n2[t]

n2[t+1] = c n2[t] + d n1[t] n2[t]

(e)
n1[t+1] = a n1[t]2

n2[t+1] = b n1[t] + c n2[t]

Describe in words how you would analyse the linear sets of equations and the non-linear sets of equations to get a sense of how the dynamical systems behave.