How to computer a frequency spectrum and find its largest spectral energy

I am given set of equation

I am suppose to plot x1 x2 and x3 as a 3d dimensional phase, but direction wants me to omit any possible initial transient trajectory.

Please help with detail explainations!

Answer 1

[Chunru]

fs = 10;
tspan = [0:1/fs:100];   % specify the time points
xint = [3.0;2.0;1.0];
[t,x]= ode45(@nonlin,tspan,xint);

% remove some trainsition part of x
t = t(100:end);
x = x(100:end, :);

subplot(211); plot(t, x)
subplot(212); plot(20*log10(abs(fft(x))))

function dxdt = nonlin(t,x)
e = 2.5;
dxdt = zeros(3,1);
dxdt(1) = -(x(2)+x(3));       
dxdt(2) = x(1) + ((1/5)*x(2));   
dxdt(3) = (1/5)+(((x(1)-e))*x(3));    
end

[PetronasAMG]

how would you remvoe the transient part in the phase portrait? not queit understanding the solution. Could it be explained more indepth?

[Chunru]

In the original code above, I did not remove the transition part. Just kept them. I update the code to remove the transistion period.