Nonlinear system (has anyone seen this equation form?)

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Jeff 2012-11-25

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https://ww2.mathworks.cn/matlabcentral/answers/54705-nonlinear-system-has-anyone-seen-this-equation-form

Has anyone seen this form of a nonlinear equation with respect to X, but linear with respect to Y & Z? I provided a contour plot within the region for all 3 variables between -2 & 2. The plot is actually Z*conjugate(Z) so that the magnitude is above ZERO. If I am correct I may have seen this before in orbital mechanics, but my undergrad years are a bit behind me. I generated this eq. during a parametric analysis of a 2nd order oscillator. I would like to come up to speed about the physical phenomena this equation might describe.

I would provide a PDF of my results, but I do not see that I can upload a file. So below is my MATLAB code. If you can provide info how to attach or upload a file please respond.

alpha=-2:0.004:2;
rho=10^-6;
for k=1:length(alpha)-1
    rho(k+1)=rho(k)*10^(12/(length(alpha)-1));
end
ones(1:k+1)=1;
X=fliplr(-1*ones'*rho);
X=[X ones'*rho];
Y=alpha'*ones;
Y=[Y Y];
z=((1-Y).*((1-Y).^2+1).*((1+Y).^2-1).^2.*X-(1+Y).*((1+Y).^2+1).*((1-Y).^2-1).^2)./(4*(1-Y).*(1+Y).*((1-Y).*(1+(1+Y).^2)-(1+Y).*((1-Y).^2+1).*X));
Z=z.*conj(z);
mesh(X,Y,Z);
[m n]=size(Z);
axis([X(1,1) X(m,n) Y(1,1) Y(m,n) 0 2 0 2])