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clear;
clear;
clc;
close;
//set(gca(),"auto_clear","off") //hold on
//Obtain the Jacobian A:
//A = [df/dx df/dy;dg/dx dg/dy]; where f=x(dot),g=y(dot)
//df/dx=partial derivative of "f" w.r.t. "x"
//Thus, A=[0 1-3(y^2); -1 -2*y];
A1=[0 1;-1 0] //Jacobian at orign
t1=det(A1)
tau1=trace(A1)
disp("Since t1>0 and tau1=0 thus orign is a linear center.")
disp("Furthermore, the system is reversible, Thus by theorem 6.6.1-->")
disp("We conclude that the orign is a nonlinear center.")
A2=[0 -2;-1 -2] //Jacobian at (-1,1)
t2=det(A2)
A3=[0 -2;-1 2] //Jacobian at (-1,-1)
t3=det(A3)
disp("Since t2=t3=-2, Thus (-1,1) and (-1,-1) are Saddle Points.")
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