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// Example 3.1.2 Pg 47
//Non-Linear Dynamics and Chaos, First Indian Edition Print 2007
//Steven H.Strogatz
clear;
clc;
close;
mtlb_hold off
for(r=0:1:3) //Varying value of parameter "r" to see number of fixed point solutions.
x=-2:0.1:3;
set(gca(),"grid",[2,5]);
mtlb_hold on
plot2d(x,exp(-x),style=-4);
plot2d(x,r-x,style=-2);
figure; //to get new graphics window
set(gca(),"grid",[2,5])
xtitle("Graph showing Number of Fix Points","X-Axis","Y-Axis");
end
disp("From the graph we get intersection point")
disp("And hence we got our FIXED POINT SOLUTION.")
disp("Clearly from graph we get stable solution when line is below exp(-x) graph.")
disp("Unstable solution when line is above exp(-x) graph.")
disp("From graph we infer that :")
disp("1. No Fixed Points for r<1")
disp("2. One Fixed Point when r=1.")
disp("3. Two Fixed Points for r>1.")
disp("hence Bifurcation Point is cleraly, r(c)=1")
mtlb_hold off
//End of Example
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