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diff --git a/27/CH3/EX3.1.1/Example_3_1_1.sce b/27/CH3/EX3.1.1/Example_3_1_1.sce
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+// Example 3.1.1, Page = 47

+// Non-Linear Dynamics and Chaos, First Indian Edition

+//Steven H. Strogatz

+// x(dot)=f(x)=r-(x^2)

+// Notation: x1,x2,x3........ are the fixed point solutions

+// since x* is an error, because of multiplication operator.

+

+clear;

+clc;

+close;

+

+for r=-1:0.1:+1                //Varying value of parameter "r" so as to obtain bifurcation diagram.

+     

+    x1 = +(sqrt(r));           //First Fixed Point.

+    x2 = -(sqrt(r));           //Second Fixed Point.

+    f1 = -2*x1;                //f'(x) at x1.

+    f2 = -2*x2;                //f'(x) at x2.

+    

+    //x(double dot) = f'(x) = -2*x.

+    set(gca(),"auto_clear","off")        //hold on

+    set(gca(),"grid",[2,5])

+    if (r<0) then

+        y = 0;    //just to draw y=0 line for r<0, as no solution

+        disp(r)

+        disp("No fixed points.")

+        plot2d(r,y,style=-2)

+    

+    else

+        set(gca(),"auto_clear","off")

+        if(f1>0)    //unstable solutions

+            disp(r,x1)

+            disp("unstable solutions")

+            plot2d(r,x1,style=-1)

+        

+        end

+        if(f1<0)    //Stable solutions

+            disp(r,x1)

+            disp("stable solutions")

+            plot2d(r,x1,style=-2)

+        

+        end

+    

+        set(gca(),"auto_clear","off")

+    

+        if(f2>0)    //unstable solutions

+            disp(r,x2)

+            disp("unstable solutions")

+            plot2d(r,x2,style=-1)

+        

+        end

+        if(f2<0)    //stable solutions

+            disp(r,x2)

+            disp("stable solutions")

+            plot2d(r,x2,style=-2)

+        

+        end

+        xtitle("Bifurcation Diagram","r-parameter","x*-fix points")

+    end

+end

+disp("Clearly from the graph x=0 is bifurcation point.")

+set(gca(),"auto_clear","on")    //hold off

+//End of Example

diff --git a/27/CH3/EX3.1.2/3_1_2.jpg b/27/CH3/EX3.1.2/3_1_2.jpg
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diff --git a/27/CH3/EX3.1.2/Example_3_1_2.sce b/27/CH3/EX3.1.2/Example_3_1_2.sce
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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;

+set(gca(),"auto_clear","on")    //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])

+    set(gca(),"auto_clear","off")    //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")

+set(gca(),"auto_clear","on")

+//End of Example

+    
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diff --git a/27/CH3/EX3.2.1/3_2_1.jpg b/27/CH3/EX3.2.1/3_2_1.jpg
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diff --git a/27/CH3/EX3.2.1/Example_3_2_1.sce b/27/CH3/EX3.2.1/Example_3_2_1.sce
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+//Example 3.2.1 Page 51

+//Non-Linear Dynamics and Chaos, First Indian Edition, Print-2007

+//Steven H. Strogatz

+

+clear;

+clc;

+close;

+

+// General INTRODUCTION

+disp("To show their is Transcritical Bifurcation show :")

+disp("1. Their are always two fixed points ,")

+disp("And they change their Stability around Bifurcation Point.")

+disp("2. Hence, the nature of given equation should be Quadratic.")

+disp("To show this use Taylor Expansion.")

+// END INTRODUCTION

+

+//By Taylor Expansion of given x(dot) and neglecting order(x^3) and higher order terms we get ----

+//x(dot) = (1-ab)x + (1/2)(ab*b)x^2.------Let x(dot) = f(x)

+

+//Stability Analysis : Put x(dot)=f(x)=0

+for(a=5)                                //Fixing one of the two parameters (i.e "a" And "b")

+    for(b=-4:0.15:3)                    //Varying another parameter to plot Bifurcation Diagram.

+        

+        x1 = 0;    //First Fixed Point

+        x2 = 2*(a*b -1)/(a*b*b);     //Second Fixed Point

+        f1 = (1-a*b);              //f'(x) at x1

+        f2 = -(1-a*b);            //f'(x) at x2

+        

+        //x(double dot)= f'(x) = (1-ab) + a(b^2)x

+        

+        set(gca(),"auto_clear","off")        //For "hold on" to plot points.

+        set(gca(),"grid",[2,5])             // To set axis

+        if(f1>0)                 //Unstable fixed point.

+            plot2d(1-a*b,x1,style=-2)

+        end

+        if(f1<0)                //Stable Fixed point.

+            plot2d(1-a*b,x1,style=-3)

+        end

+        if(f2>0)                //Unstable Fixed Point.

+            plot2d(1-a*b,x2,style=-2)

+        end

+        if(f2<0)                //Stable Fixed Point.

+            plot2d(1-a*b,x2,style=-3)

+        end

+        xtitle("Bifurcation Diagram","x-axis (1-a*b)","x*-fix points")

+    end

+end

+disp("From Graph it is clearly visible that the two fixed points changes stability around point ab=1 ")

+

+set(gca(),"auto_clear","on")    //for hold off

+

+//end of Example
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diff --git a/27/CH3/EX3.2.2/3_2_2.jpg b/27/CH3/EX3.2.2/3_2_2.jpg
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diff --git a/27/CH3/EX3.2.2/Example_3_2_2.sce b/27/CH3/EX3.2.2/Example_3_2_2.sce
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+//Example 3.2.2 Page 52

+//Non-Linear Dynamics and Chaos, First Indian Edition, Print-2007

+//Steven H. Strogatz

+

+clear;

+clc;

+close;

+

+//General INTRODUCTION

+disp("To show their is Transcritical Bifurcation show :")

+disp("1. Their are always two fixed points ,")

+disp("And they change their Stability around Bifurcation Point.")

+disp("2. Hence, the nature of given equation should be Quadratic.")

+disp("To show this use Taylor Expansion.")

+// End INTRODUCTION

+

+// u(dot) = (r+1)u - (1/2)r(u^2) + O(u^3)

+// u(dot) = (r+1)u - (1/2)r(u^2) + ZERO -----neglecting higher order terms

+// Let u(dot) = f(u)

+

+for r=-4:0.15:3        //Varying Parmater "r" to obtain Bifurcation Diagram

+    u1 = 0;            //First Fixed Point.

+    u2 = 2*(r+1)/r;    //Second Fixed Point.

+    f1 = (r+1);        //f'(u) at u1

+    f2 = -(r+1);       //f'(u) at u2

+    set(gca(),"auto_clear","off")    //hold on

+    set(gca(),"grid",[2,5])

+    

+    //u(double dot) = f'(u) = (r+1) - r*u

+    

+    if (f1>0) then    //Unstable Fixed Point.

+        plot2d(r+1,u1,style=-2)

+    end

+    if (f1<0) then    //Stable Fixed Point.

+        plot2d(r+1,u1,style=-3)

+    end

+    if (f2>0) then    //Unstable Fixed Point.

+        plot2d(r+1,u2,style=-2)

+    end

+    if (f2<0) then    //Stable Fixed Point.

+        plot2d(r+1,u2,style=-3)

+    end

+    xtitle("Bifurcation Diagram","x-Axis -(r+1)","u*-fix points")

+end

+set(gca(),"auto_clear","on")    //hold off

+disp("Clearly from the Bifurcation Diagram we see that r=-1 is the bifurcation point.")

+//end of Example
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diff --git a/27/CH3/EX3.4.1/3_4_1.jpg b/27/CH3/EX3.4.1/3_4_1.jpg
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diff --git a/27/CH3/EX3.4.1/3_4_1_2.jpg b/27/CH3/EX3.4.1/3_4_1_2.jpg
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diff --git a/27/CH3/EX3.4.1/Example_3_4_1.sce b/27/CH3/EX3.4.1/Example_3_4_1.sce
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+//Example 3.4.1 Page 57

+//Non-Linear Dynamics and Chaos, First Indian Edition Print 2007

+//Steven H. Strogatz

+

+clear;

+clc;

+close;

+set(gca(),"auto_clear","on")    //hold off

+

+for (B=0.5:0.5:2)    //Capital "B" is denoting Beta.

+    x=-3:0.1:3;

+    y=x;            //To plot x=y line.

+    

+    figure;

+    set(gca(),"auto_clear","off")    //hold on

+    set(gca(),"grid",[2,5])

+    plot2d(x,y,style=-4)

+    plot2d(x,B*tanh(x),style=-1)

+    xtitle("Intersection For different Beta values","x-Axis","y-Axis")

+    

+    

+end

+disp("From graph following points are clear:")

+disp("1. For B<1, only orign is the fixed point.")

+disp("2. For B>1, their are two new fixed points.")

+

+//Stability

+figure

+set(gca(),"grid",[2,5])

+for(x1 = -3:0.5:3)

+    if(x1~=0)

+    B = x1/tanh(x1);

+    plot2d(B,x1,style=-4)

+end

+

+for(B=0:0.1:3);

+    x1 = 0;

+if(B<1)

+    plot2d(B,x1,style=-4)    //Stable

+else

+    plot2d(B,x1,style=-2)    //Unstable

+end  

+xtitle("Bifurcation Diagram","Beta Values-Parameter","x*-Fix Points")

+end

+end

+set(gca(),"auto_clear","on")

+//If B<1 then only one fixed point.

+//end of Example.
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diff --git a/27/CH3/EX3.4.2/3_4_2.jpg b/27/CH3/EX3.4.2/3_4_2.jpg
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diff --git a/27/CH3/EX3.4.2/Example_3_4_2.sce b/27/CH3/EX3.4.2/Example_3_4_2.sce
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+//Example 3.4.2 Page 58

+//Non-Linear Dynamics and Chaos First Indian Edition Print 2007

+//Steven H.Strogatz

+clear;

+clc;

+close;

+set(gca(),"auto_clear","on")    //hold off

+

+for(r=-1:0.5:1)

+    x = -3:0.1:3;

+    V = -0.5*r*(x^2)+0.25*(x^4);

+    set(gca(),"auto_clear","off")    //hold on

+    xtitle("Potential Diagram","X-Axis","Y-Axis")

+    plot2d(x,V,style=-4)

+    figure

+    set(gca(),"grid",[2,5])

+    

+end

+set(gca(),"auto_clear","on")

+//End of Example
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