behaviour of an expression

I have an expression with piecewise functions. the code looks like:

function a()
  %some constants here

    f = 0:0.001:20;
    r1 = 0.05;
    p = something-f.*(something/something);
    for i=1:100
        r1= R(p);
    end
    for i=1:100
        r1 = R(P);
        y1(k,:) = r1;
    end
    y1=sort(y1)
    plot(f,y1,'k.','MarkerSize',1)
    xlabel('f')
    ylabel('r1');
    set(gca,'xlim',[0 20]);

    %piecewise functions here
    function r = R(P)
        r = NaN(size(P));
        r(P<=0) = sqrt((somthing)*(1-P(P<=0)/something).^-2);
        r(P>0) = sqrt((somthing)-(somthing)*(1-P(P>0)/somthing).^-5);
     end

end

My friend said the behaviour will be like the logistic map. but after printing, I found it just looks like a curve.

Did I make any mistakes in the code? Please help me

Kind Regards