Problem 1: First, perform a detailed (linear) stability analysis of the fixed points of the system of differential equations dx dt dy dt = X x(1 x - y) = y (x ), where it is supposed that the functions x(t) and y(t) that satisfy the system are non-negative for all t 0. The two parameters in the system, and , are both taken to be strictly positive. Next, obtain the Euler discretisation of this system and perform a linear stability analysis for its fixed points. This last analysis need not be completely exhaustive but you should discuss any discretisation-induced effects on the stability or instability of the fixed points.