initial commit / add all books

15 files changed, 240 insertions, 0 deletions

diff --git a/27/CH8/EX8.1.1/8_1_1.jpg b/27/CH8/EX8.1.1/8_1_1.jpg
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diff --git a/27/CH8/EX8.1.1/8_1_1_2.jpg b/27/CH8/EX8.1.1/8_1_1_2.jpg
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diff --git a/27/CH8/EX8.1.1/Example_8_1_1.sce b/27/CH8/EX8.1.1/Example_8_1_1.sce
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+clear;

+clear;

+clc;

+close;

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

+

+a=0.4;

+b=0.8;

+for x=0:0.1:3

+    y1=a*x;

+    y2=(x^2)/(b*(1+x^2));

+    plot2d(x,y1,style=-2)

+    plot2d(x,y2,style=-3)

+end

+

+// Classification of fixed points :

+

+A1=[-a 1;0 -b]                //Jacobian at (0,0)

+T=trace(A1)                    //Trace of A

+D=det(A1)                      //Determinant of A

+

+disp("Since, D>0, T<0 , orign is always a fixed point.")

+

+//Now using the arguments given in book and the figure obtained through this example, we conclude :

+

+disp("Middle Fixed Point lies between 0<x*<1, Thus is a Saddle Point.")

+disp("The Thied fixed point is with x*>1, Thus always a stable node.")

+

+xtitle("Nullclines--Showing Intersection of x(dot) and y(dot)","x-Axis ( x )","y-Axis ( y )")

+figure

+a=0.4;

+b=0.8;

+  function xd=linear811(t,x)

+    xd(1)=-a*x(1)+x(2);

+    xd(2)=((x(1)^2)/(1+x(1)^2))-b*x(2);

+             //x(dot);   x(2) means y.

+             //y(dot);   x(1) means x.; 

+  endfunction

+  bound=[0,0,4,4];        //Bounds of x-axis and y-axis as [xmin ymin xmax ymax], change them according to your needs.

+  nrect=20;     //increase it to get more number of curves, i.e. more information will be available.

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

+  x=linspace(bound(1),bound(3),nrect);

+  y=linspace(bound(2),bound(4),nrect);

+  x0=[];

+ 

+ for i=1:20

+     x0=[x(i);y(i)];

+     t0=0;

+     t=0:0.01:3000;

+     xout=ode(x0,t0,t,linear811);

+     plot2d(xout(1,:),xout(2,:));

+ end

+  xtitle('Phase Portrait','x-axis ( x )','y-axis ( y )')
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diff --git a/27/CH8/EX8.1.2/8_1_2.jpg b/27/CH8/EX8.1.2/8_1_2.jpg
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diff --git a/27/CH8/EX8.1.2/8_1_2_2.jpg b/27/CH8/EX8.1.2/8_1_2_2.jpg
new file mode 100755
index 000000000..80061fd92
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diff --git a/27/CH8/EX8.1.2/Example_8_1_2.sce b/27/CH8/EX8.1.2/Example_8_1_2.sce
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+clear;

+clear;

+clc;

+close;

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

+

+//f = x(dot)

+//g = y(dot)

+//Obtain Jacobian as :

+//J=[df/dx  df/dy; dg/dx  dg/dy]

+//Thus, J=[mew-3*x^2  0; 0  -1]

+mew=2;

+subplot(221)

+for x=-2:0.1:2

+    y1=(mew*x)-x^3;

+    y2=0;

+    plot2d(x,y1,style=-2)

+    plot2d(x,y2,style=-3)

+end

+xtitle("Nullclines--Showing Intersection of x(dot) and y(dot) for mew > 0","x-Axis ( x )","y-Axis ( y )")

+//Stabilities for mew >0

+A1=[mew 0;0 -1]            //Jacobian at (0,0)

+T1=trace(A1)

+D1=det(A1)

+A2=[-2*mew 0;0 -1]        //Jacobian at (+sqrt(mew),0) and (-sqrt(mew),0)

+T2=trace(A2)

+D2=det(A2)

+Det = (T2^2) - 4*D2

+

+disp("Since D1<0, Thus (0,0) is a Saddle Point.")

+disp("Since T2<0, D2>0 and Det>0, thus (+sqrt(mew),0) and (-sqrt(mew),0) are stable points.")

+subplot(224)

+mew=-2;

+for x=-2:0.1:2

+    y1=(mew*x)-x^3;

+    y2=0;

+    plot2d(x,y1,style=-2)

+    plot2d(x,y2,style=-3)

+end

+xtitle("Nullclines--Showing Intersection of x(dot) and y(dot) for mew < 0","x-Axis ( x )","y-Axis ( y )")

+// Classification of fixed points :

+

+A3=[mew 0;0 -1]                //Jacobian at (0,0)

+T3=trace(A3)                    //Trace of A

+D3=det(A3)                      //Determinant of A

+Det3=T3^2 - 4*D3

+disp("Since, D>0, T<0 , and Det3>0 orign is a stable fixed point.")

+

+

+//Note Stabilities can be deduced from the figures also as done in previous chapters.

+figure

+mew=-4;

+  function xd=linear812(t,x)

+    xd(1)=mew*x(1)-(x(1)^3);

+    xd(2)=-x(2);

+             //x(dot);   x(2) means y.

+             //y(dot);   x(1) means x.; 

+  endfunction

+  bound=[-4,-4,4,14];        //Bounds of x-axis and y-axis as [xmin ymin xmax ymax], change them according to your needs.

+  nrect=10;     //increase it to get more number of curves, i.e. more information will be available.

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

+  x=linspace(bound(1),bound(3),nrect);

+  y=linspace(bound(2),bound(4),nrect);

+  x0=[];

+ 

+ for i=1:10

+     x0=[x(i);y(i)];

+     t0=0;

+     t=0:0.01:3000;

+     xout=ode(x0,t0,t,linear812);

+     plot2d(xout(1,:),xout(2,:));

+ end

+  xtitle('Phase Portrait','x-axis ( x )','y-axis ( y )')

diff --git a/27/CH8/EX8.1.3/8_1_3.jpg b/27/CH8/EX8.1.3/8_1_3.jpg
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index 000000000..6ef3e3594
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+++ b/27/CH8/EX8.1.3/8_1_3.jpg
diff --git a/27/CH8/EX8.1.3/Example_8_1_3.sce b/27/CH8/EX8.1.3/Example_8_1_3.sce
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index 000000000..bf0bb81aa
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+++ b/27/CH8/EX8.1.3/Example_8_1_3.sce
@@ -0,0 +1,22 @@
+mew=-2.1;

+  function xd=linear813(t,x)

+    xd(1)=mew*x(1)+x(2)+sin(x(1));

+    xd(2)=x(1)-x(2);

+             //x(dot);   x(2) means y.

+             //y(dot);   x(1) means x.; 

+  endfunction

+  bound=[-2,-2,2,2];        //Bounds of x-axis and y-axis as [xmin ymin xmax ymax], change them according to your needs.

+  nrect=20;     //increase it to get more number of curves, i.e. more information will be available.

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

+  x=linspace(bound(1),bound(3),nrect);

+  y=linspace(bound(2),bound(4),nrect);

+  x0=[];

+ 

+ for i=1:20

+     x0=[x(i);y(i)];

+     t0=0;

+     t=0:0.01:3000;

+     xout=ode(x0,t0,t,linear813);

+     plot2d(xout(1,:),xout(2,:));

+ end

+  xtitle('Phase Portrait','x-axis ( x )','y-axis ( y )')
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diff --git a/27/CH8/EX8.2.1/8_2_1.jpg b/27/CH8/EX8.2.1/8_2_1.jpg
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diff --git a/27/CH8/EX8.2.1/Example_8_2_1.sce b/27/CH8/EX8.2.1/Example_8_2_1.sce
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index 000000000..df7d9cc11
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+++ b/27/CH8/EX8.2.1/Example_8_2_1.sce
@@ -0,0 +1,22 @@
+mew=-0.2;

+  function xd=linear821(t,x)

+    xd(1)=mew*x(1)-x(2)+x(1)*x(2)^2;

+    xd(2)=x(1)+mew*x(2)+x(2)^3;

+             //x(dot);   x(2) means y.

+             //y(dot);   x(1) means x.; 

+  endfunction

+  bound=[-0.8,-0.8,0.8,0.8];        //Bounds of x-axis and y-axis as [xmin ymin xmax ymax], change them according to your needs.

+  nrect=35;     //increase it to get more number of curves, i.e. more information will be available.

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

+  x=linspace(bound(1),bound(3),nrect);

+  y=linspace(bound(2),bound(4),nrect);

+  x0=[];

+ 

+ for i=1:35

+     x0=[x(i);y(i)];

+     t0=0;

+     t=0:0.01:3000;

+     xout=ode(x0,t0,t,linear821);

+     plot2d(xout(1,:),xout(2,:));

+ end

+  xtitle('Phase Portrait','x-axis ( x )','y-axis ( y )')
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diff --git a/27/CH8/EX8.3.1/8_3_1.jpg b/27/CH8/EX8.3.1/8_3_1.jpg
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diff --git a/27/CH8/EX8.3.1/Example_8_3_1.sce b/27/CH8/EX8.3.1/Example_8_3_1.sce
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+++ b/27/CH8/EX8.3.1/Example_8_3_1.sce
@@ -0,0 +1,23 @@
+a=10;

+b=3;

+  function xd=linear831(t,x)

+    xd(1)=a-x(1)-((4*x(1)*x(2))/(1+x(1)^2));

+    xd(2)=(b*x(1))*(1-(x(2)/(1+x(1)^2)));

+             //x(dot);   x(2) means y.

+             //y(dot);   x(1) means x.; 

+  endfunction

+  bound=[0,3,3,7];        //Bounds of x-axis and y-axis as [xmin ymin xmax ymax], change them according to your needs.

+  nrect=25;     //increase it to get more number of curves, i.e. more information will be available.

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

+  x=linspace(bound(1),bound(3),nrect);

+  y=linspace(bound(2),bound(4),nrect);

+  x0=[];

+ 

+ for i=1:25

+     x0=[x(i);y(i)];

+     t0=0;

+     t=0:0.01:3000;

+     xout=ode(x0,t0,t,linear831);

+     plot2d(xout(1,:),xout(2,:));

+ end

+  xtitle('Phase Portrait','x-axis ( x )','y-axis ( y )')
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diff --git a/27/CH8/EX8.3.2/8_3_2.jpg b/27/CH8/EX8.3.2/8_3_2.jpg
new file mode 100755
index 000000000..785a61e38
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+++ b/27/CH8/EX8.3.2/8_3_2.jpg
diff --git a/27/CH8/EX8.3.2/8_3_2_2.jpg b/27/CH8/EX8.3.2/8_3_2_2.jpg
new file mode 100755
index 000000000..c8347f243
--- /dev/null
+++ b/27/CH8/EX8.3.2/8_3_2_2.jpg
diff --git a/27/CH8/EX8.3.2/Example_8_3_2.sce b/27/CH8/EX8.3.2/Example_8_3_2.sce
new file mode 100755
index 000000000..0662cb864
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+++ b/27/CH8/EX8.3.2/Example_8_3_2.sce
@@ -0,0 +1,47 @@
+a=10;

+b=4;

+  function xd=linear832(t,x)

+    xd(1)=a-x(1)-((4*x(1)*x(2))/(1+x(1)^2));

+    xd(2)=(b*x(1))*(1-(x(2)/(1+x(1)^2)));

+             //x(dot);   x(2) means y.

+             //y(dot);   x(1) means x.; 

+  endfunction

+  bound=[0,0,4,10];        //Bounds of x-axis and y-axis as [xmin ymin xmax ymax], change them according to your needs.

+  nrect=10;     //increase it to get more number of curves, i.e. more information will be available.

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

+  x=linspace(bound(1),bound(3),nrect);

+  y=linspace(bound(2),bound(4),nrect);

+  x0=[];

+ 

+ for i=1:10

+     x0=[x(i);y(i)];

+     t0=0;

+     t=0:0.01:3000;

+     xout=ode(x0,t0,t,linear832);

+     plot2d(xout(1,:),xout(2,:));

+ end

+  xtitle('Phase Portrait','x-axis ( x )','y-axis ( y )')

+  figure

+  a=10;

+b=2;

+  function xd=linear8322(t,x)

+    xd(1)=a-x(1)-((4*x(1)*x(2))/(1+x(1)^2));

+    xd(2)=(b*x(1))*(1-(x(2)/(1+x(1)^2)));

+             //x(dot);   x(2) means y.

+             //y(dot);   x(1) means x.; 

+  endfunction

+  bound=[0,0,5,8];        //Bounds of x-axis and y-axis as [xmin ymin xmax ymax], change them according to your needs.

+  nrect=10;     //increase it to get more number of curves, i.e. more information will be available.

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

+  x=linspace(bound(1),bound(3),nrect);

+  y=linspace(bound(2),bound(4),nrect);

+  x0=[];

+ 

+ for i=1:10

+     x0=[x(i);y(i)];

+     t0=0;

+     t=0:0.01:3000;

+     xout=ode(x0,t0,t,linear8322);

+     plot2d(xout(1,:),xout(2,:));

+ end

+  xtitle('Phase Portrait','x-axis ( x )','y-axis ( y )')
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