How to find eigen values of Fischer's equation?
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Just like we have eigen values for heat equation as lambda=n*pi/l type. How can we find eigen values for the Fischer's equation. I'm attaching the file in which I've attempted to do so? But I'm not sure if it's correct?
![](/matlabcentral/answers/uploaded_files/1683046/Screenshot_2024-04-30-17-37-30-099_com.google.android.apps.docs.jpg)
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Torsten
on 1 May 2024
I don't know how eigenvalues of the nonlinear Fisher's equation are mathematically defined. Can you show us the equation with the "lambda" in it ?
Sam Chak
on 1 May 2024
@simran, Sometimes we get confused when we first start to learn a new material. This is normal. What are the eigenvalues of the linearized dynamical system? Since the nonlinear Fisher equation contains only one nonlinear term, I visualized the linear approximation around a selected operating point at
.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1683796/image.png)
x = linspace(0, 1, 101); % range of x
f = @(x) x.*(1 - x).*x; % nonlinear function
xop = 1/3; % operating point
Lin = 1/3*(x - xop) + f(xop); % linear approximation around xop
plot(x, f(x), x, Lin), grid on
title('Linear approximation of f(\phi) at \phi = 1/3')
xlabel('\phi'), legend('Nonlinear', 'Linear', 'location', 'northwest', 'fontsize', 14)
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