What the connection of 'phase plot' to mathematics? Is there a connection beteen this subject to math?
You should give a bit more information- the word "phase" and the phrase "phase plot" may have many different meanings in various sciences. In "mechanics", specifically, we can think of position and momentum of an object as separate, independent, variables; the two variables together giving the "phase" of the object. In that case, a "phase plot" is a graph showing the position on one axis and the momentum on another. It's connection with mathematics is the connection of any graph with mathemtics- together, of course, with whatever mathematical formula are used in physics to connect position and momentum.