How to plot the trajectories of the equilibrium points
6 vues (au cours des 30 derniers jours)
Afficher commentaires plus anciens
I want to plot the trajectories of the equilibrium points and to show the stability of them . This my code to find all the equilibrium points
r1=576; r2=23616/11; r3=39456/11;
a1=572; a2=4420; a3=5850;
b1=308; b2=1804; b3=2970;
c1=b1; c2=b1; c3=594;
syms x y z
vars = [x, y, z];
eqs=[(r1-a1*x-b1*y-c1*z)*x,(r2-a2*x-b2*y-c2*z)*y,(r3-a3*x-b3*y-c3*z)*z];
[xc, yc, zc] = solve(eqs(1), eqs(2), eqs(3));
[xc, yc, zc]
A = jacobian(eqs, vars);
disp('Matrix of linearized system:')
subs(A, vars, [xc(1), yc(1),zc(1)])
disp('eigenvalues:')
eig(ans)
disp('Matrix of linearized system:')
subs(A, vars, [xc(2), yc(2),zc(2)])
disp('eigenvalues:')
eig(ans)
disp('Matrix of linearized system:')
subs(A, vars, [xc(3), yc(3),zc(3)])
disp('eigenvalues:')
eig(double(ans))
disp('Matrix of linearized system:')
subs(A, vars, [xc(5), yc(5),zc(5)])
disp('eigenvalues:')
eig(ans)
disp('Matrix of linearized system:')
subs(A, vars, [xc(6), yc(6),zc(6)])
disp('eigenvalues:')
eig(ans)
disp('Matrix of linearized system:')
subs(A, vars, [xc(7), yc(7),zc(7)])
disp('eigenvalues:')
eig(ans)
disp('Matrix of linearized system:')
subs(A, vars, [xc(8), yc(8),zc(8)])
disp('eigenvalues:')
eig(ans)
there are 8 equilibrium points and one of them is negative so we do not care about it . Can you please help me how to plot these as the below graph. any help would be appreciated.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/160492/image.jpeg)
0 commentaires
Réponses (1)
Mischa Kim
le 8 Avr 2016
Modifié(e) : Mischa Kim
le 8 Avr 2016
Raja, you are probably best off to solving differential equations of the system for different initial conditions (and the plot the solutions). You would pick the initial conditions close to the equilibrium points to get the figure you show above. See for example this answer.
Voir également
Catégories
En savoir plus sur Graph and Network Algorithms dans Help Center et File Exchange
Produits
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!