Currency Exchange Rate Model: Paul Brunovsky. [16] proposed a mathematical model on the short time fluctuation of an asset, namely, the price of a foreign currency in a domestic reference, that is, foreign exchange rate. The model is given by the delay differential equation dx/dt = a [x (t) - x (t 1)] - |x (t)| x (t) where x(t) is the deviation of the value of a foreign currency and a > 0 is the parameter which measures the sensitivity to the changes in exchange rate. Show that the model has a single non-hyperbolic steady state solution x* - 0 for a > 0 and the equilibrium solution x* -0 is asymptotically stable for a 1, the system shows a periodic behavior