Vazquez and Redner (2004, p8489) mention a highly simplified model of political opinion dynamics consisting of population of leftists, rightists, and centrists. The leftists and rightists never talk to each other; they are too far apart politically to even begin a dialogue_ But they do talk to the centrists this is how opinion change occurs_ Whenever an extremist of either type talks with a centrist. one of them convinces the other to change his or her mind. with the winner depending OI the sign of the parameter r. If r > 0, the extremist always wins and persuades the centrist to move t0 that end of the spectrum_ If r < 0, the centrist always wins and pulls the extremist to the middle. The model s governing equations are =TIZ, y = ry~, =_IZ Ty~. Page 2 of 3 Math 119a where €,y; and are the relative fractions of rightists; leftists and centrists_ respectively; in the population: Show that the set 1 +y+2 = [ is invariant_ Analyze the long term behavior predicted by the model for both positive and negative values of r. Interpret the results in political terms_