Stability Analysis (Dertermining the Limit Cycle)

11 次查看（过去 30 天）
Macaulay Wright
Macaulay Wright 2020-4-1
评论： Star Strider 2020-4-1
I am wanting to use a simple stability analysis technique to determine the limit cycle stability for mu< 0, for my Van Der Pol oscillator. I was ideally attempting to use a phase portrait but I don't know how to produce this in code.
The matlab code I currently have produced for the Van Der Pol oscillation can be seen below.
Any guidance would be greatly appreciated.
% Simulation parameters
DT = 0.01; % Time step
N = 10000; % Number of discrete time points
% Equation parameter
mu = 0.1;
% Declare array to store discrete time samples
x = zeros(1,N);
% Set boundary conditions
x(1) = -0.01;
x(2) = 0.0;
% Simulate using recurrance relation
for i = 3:N
phi = mu*DT/2*(x(i-1)^2-1);
x(i) = x(i-1)*(2-DT^2)/(1+phi) - x(i-2)*(1-phi)/(1+phi);
end
% Plot
plot((1:N)*DT,x,'r')
% Calculating angular frequency (omega) using period
[pks,pktimes] = findpeaks(x, (1:N)*DT);
Period = mean(diff(pktimes))
Omega = (2*pi)/Period

请先登录，再回答此问题。

采纳的回答

Star Strider
Star Strider 2020-4-1
The phase portrait is usually plotted as the function against its derivative. Use the gradient function to calculate the derivative:
figure
plot(x, gradient(x))
grid
Another way is to plot the vector against a delayed version of itself:
Ofst = 5;
figure
plot(x(1:end-Ofst), x(Ofst+1:end))
grid
Both of these produce a reough phase portrait. The gradient version is likely more accurate.
  2 个评论
Macaulay Wright
Macaulay Wright 2020-4-1
Thank you again! You're a real help. It worked perfectly and it was exactly what I was trying to produce.

请先登录，再进行评论。

更多回答（0 个）

类别

在 Help Center 和 File Exchange 中查找有关 MATLAB 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by