Adapted from Stogatz] The logistic map is a simple model for a population growth. A more realistic model accounts for the so-called (strong) Allee effect, a phenomenon that correlates the size of the population to its growth rate. For the logistic map, we have seen how the growth rate decreases monotonically with the population size. The Allee effect accounts for the fact that (i) if there are too little individuals the population may extinct, and that (ii) there is an optimal population size at which the growth rate is maximized. Show that the dynamical system = ( ( )2) accounts for the Allee effect if > 0, > 0 and >/-explaintheseconditionsbasedonthegraphofthegrowthrate/.Howdothe trajectories () behave for various initial conditions?