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//Example 4.3.1 Page 97
//Non-Linear Dynamics and Chaos, First Indian Edition Print 2007
//Steven H. Strogatz
clear;
clc;
close;
set(gca(),"auto_clear","off") //hold on
// Theta(dot) = f = w - a*sin(Theta)
//a>w
//Lets take w=2, a=5;
for Theta=-%pi:0.1:%pi
f=2 - (5*sin(Theta)); //f = w-a*sin(Theta)
plot2d(Theta,f,style=-2)
end
///////////////// Figure Characteristics //////////////////////////
set(gca(),"grid",[2,5]) //Grid on
for Theta=-2*%pi:0.4:2*%pi
plot2d(Theta,0,style=-1) //Just to plot X-Axis.
plot2d(0,Theta,style=-1) //Just to plot Y-Axis.
end
plot2d(0.41,0,style=-4) //Just to Show that the Fixed point is Stable.
plot2d(2.75,0,style=-3) //Just to Show that the Fixed point is UnStable.
plot2d(1.5,0,style=-13) //Just to Show the Flow.
plot2d(-2,0,style=-12) //Just to Show the Flow.
plot2d(3.2,0,style=-12) //Just to Show the Flow.
xtitle("Theta(dot) = w - a*sin(Theta), for a > w","X-Axis","Y-Axis")
//////////////////////////////////////////////////////////////////
exec circle.sci //function to draw circle is executed
figure(1) //Graphic Window(1)
circle([0 0],4,50) //Circle is drawn with (0,0)as center, radius=4.
///////////////// figure Properties /////////////////////////
a=get("current_axes");//get the handle of the newly created axes
a.data_bounds=[-5,-5;5,5];
set(gca(),"grid",[2,5])
plot2d(0,4,style=-12) //Showing Vector Fields on Circle
plot2d(4,0,style=-6) //Showing Vector Fields on Circle
plot2d(-3,2.6,style=-3) //Showing Unstable-Fixed Point with plus inside a circle
plot2d(3,2.6,style=-4) //Showing Stable Fixed Point with diamond
xtitle("Vector Field on Circle for a > w","X - Axis","Y - Axis")
/////////////////////////////////////////////////////////////
//End of Example_4_3_1.
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